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# Recent problems solved by 'drj'

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 Expressions-with-variables/227843: x + y = 7 x + 3y = 111 solutions Answer 169270 by drj(1380)   on 2009-10-17 11:59:00 (Show Source): You can put this solution on YOUR website! Equation A Equation B Step 1. Subtract Equation A from Equation B (or Equation B - Equation A) to eliminate x Step 2. Divide by 2 to both sides of the equation Step 3. Now Substitute into equation A to find x Subtract 2 from both sides to get x. Step 4. Now we have and as a solution. Check to see if this also satisfies equation B . which is a true statement Step 5. ANSWER: The solution is and . Or the intersection point between these two lines is (5,2). See graph below, I hope the above steps were helpful. For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV http://www.Facebook.com/FreedomUniversity.TV http://www.Twitter.com/FreedomUTV
Equations/227853: 5x+3y=12
8x+3y=9
1 solutions

Answer 169267 by drj(1380)   on 2009-10-17 11:39:33 (Show Source):
You can put this solution on YOUR website!
5x+3y=12
8x+3y=9

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 3*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

http://www.FreedomUniversity.TV

Equations/227780: Can you help me Solve the problem by using addition/elimination?
1.8x-2y=0.9
0.04x+0.18y=0.15
1 solutions

Answer 169228 by drj(1380)   on 2009-10-17 00:31:13 (Show Source):
You can put this solution on YOUR website!
Can someone pls show me how to solve this equation using the addition/elimination process?

1.8x-2y=0.9 Equation A
0.04x+0.18y=0.15 Equation B

Step 1. Multiply by 0.09 to Equation A to both sides of the equation

Equation A1
Equation B
Step 2. Add Equations A1 and B to eliminate the y terms.

Step 3. Divide by 0.202 to both sides of the equation

Step 4. Substitute into Equation A to solve for y.

Step 5. Add 2y-0.9 to both sides of the equation

Step 6. Divide by 2 to both sides of the equation

Step 7. ANSWER: The solution is and

As a check, use the substitution shown below which have the same results.

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving -2*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

Equations/227783: How do I sovle the system?
2x+5y=1
-x+6y=8
1 solutions

Answer 169226 by drj(1380)   on 2009-10-17 00:28:16 (Show Source):
You can put this solution on YOUR website!
How do I solve the system?
2x+5y=1
-x+6y=8

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 5*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

 Equations/227782: How would I solve for x? -3x+6(x+4)=91 solutions Answer 169225 by drj(1380)   on 2009-10-17 00:25:19 (Show Source): You can put this solution on YOUR website!How would I solve for x? Step 1. Multiply to get rid of the parenthesis. Step 2. Combine x-terms Step 3. Subtract 24 from both sides of the equation Step 4. Divide by 3 to both sides of the equation Step 5. Substitute into the original equation to check solution. which is a true statement. Step 6. ANSWER: Solution is . I hope the above steps were helpful. For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
 Evaluation_Word_Problems/227778: The perimeter of a rectangle is 106 inches. The length exceeds the width by 45 inches. Find the length and the width. The length is ____ inches. (Type an integer or a decimal) 1 solutions Answer 169224 by drj(1380)   on 2009-10-17 00:13:53 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangle is 106 inches. The length exceeds the width by 45 inches. Find the length and the width. The length is 49 inches. (Type an integer or a decimal) Step 1. The perimeter P means adding up all the four sides of a rectangle. Step 2. Let w be the width. Step 3. Let w+45 be the length Step 4. Then, P=w+w+w+45+w+45=106. Step 5. Solving yields the following steps Subtract 90 form both sides of the equation Divide by 4 to both sides of the equation. For , then and check which is a true statement. Step 6. ANSWER: The length is 49 inches. I hope the above steps were helpful. For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J
1. A SQUARE AND RECTANGLE HAVE EQUAL AREAS. IF THE RECTANGLE IS 36 BY 16, WHAT IS THE SIDE OF A SQUARE?
2.IN A SOCIAL HALL OF A BUILDING, THERE ARE 150 SEATS ARRANGED IN ROWS WITH 5 MORE SEATS PER ROW THAN THE NUMBER OF ROWS. HOW MANY SEATS ARE THERE IN EACH ROW?
THANK YOU!!! I REALLY APPRECIATE IT...
1 solutions

Answer 169223 by drj(1380)   on 2009-10-16 23:16:01 (Show Source):
You can put this solution on YOUR website!
Problem 1. A SQUARE AND RECTANGLE HAVE EQUAL AREAS. IF THE RECTANGLE IS 36 BY 16, WHAT IS THE SIDE OF A SQUARE?

Step 1. The area of a rectangle A=36*16=576 (area=base*height}}}

Step 2. The square has equal sides where we let s be the side which is equal to the base and height so A=s*s=s^2.

Step 3. The areas are equal in Steps 1 and 2. Then

Step 4. Take the square root to both sides of the equation or .

Step 5. ANSWER: The side of the square is 24.

Problem 2. IN A SOCIAL HALL OF A BUILDING, THERE ARE 150 SEATS ARRANGED IN ROWS WITH 5 MORE SEATS PER ROW THAN THE NUMBER OF ROWS. HOW MANY SEATS ARE THERE IN EACH ROW?

Step 1. Let n be the number of rows.

Step 2. Let n+5 be the number of seats per row.

Step 3. Then, n(n+5)=150 since there are 150 seats.

Step 4. Subtract 150 to both sides of equation in Step 3.

Step 5. To solve, use the quadratic equation given as

where a=1, b=5, and c=-150

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=625 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 10, -15. Here's your graph:

Selecting the positive solution of and and note the product is 150 seats.

Step 6. ANSWER: The number of seats in each row is 15 seats.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

 Linear-equations/227768: 1. By looking at two linear equations, is there a way you can you tell if the corresponding lines are parallel? 1 solutions Answer 169220 by drj(1380)   on 2009-10-16 22:43:58 (Show Source): You can put this solution on YOUR website!By looking at two linear equations, is there a way you can you tell if the corresponding lines are parallel? Step 1. Two lines are parallel when they have the same slope, say m. Step 2. So the two linear equations should be in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b). Step 3. Example: y=2x+3 and y=2x-9. These two line are parallel since the slope is m=2. I hope the above steps were helpful. For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J drjctu@gmail.com http://www.FreedomUniversity.TV http://www.Facebook.com/FreedomUniversity.TV http://www.Twitter.com/FreedomUTV
 Polynomials-and-rational-expressions/227759: What is the LCM of 5(x-3) and 15(x-3).1 solutions Answer 169219 by drj(1380)   on 2009-10-16 22:40:07 (Show Source): You can put this solution on YOUR website!What is the LCM of 5(x-3) and 15(x-3). Step 1. The Least Common Multiple is the smallest number that is a multiple of two or more numbers. Step 2. In this example, looking first at the numbers, the Least Common Multiple of 5 and 15 is 15, because 15 is a multiple of 15 and also a multiple of 5. Step 3. Also x-3 is the least common multiple between the two terms. Step 4. ANSWER: The LCM is 15(x-3). I hope the above steps were helpful. For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV http://www.Facebook.com/FreedomUniversity.TV http://www.Twitter.com/FreedomUTV
Rectangles/227757: Suppose that the length of a rectangle is three cm longer than twice the width and that the perimeter of the rectangle is 90 cm.
a) Set up an equation for the perimeter involving only W, the width of the rectangle.

1 solutions

Answer 169217 by drj(1380)   on 2009-10-16 22:33:38 (Show Source):
You can put this solution on YOUR website!
Suppose that the length of a rectangle is three cm longer than twice the width and that the perimeter of the rectangle is 90 cm.

Step 1. The perimeter P means adding up all the four sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let 2w+3 be the length since the length is three cm longer than twice the width.

Step 4. Then, P=w+w+2w+3+2w+3=90.

Step 5. Solving yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: w=14. Graphical form: Equation was fully solved.Text form: w+w+2w+3+2w+3=90 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( w+w+2w+3+2w+3=90 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
It becomes .

Look at .
Moved to the right of expression
It becomes .

Look at .
Eliminated similar terms ,,, replacing them with
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Moved these terms to the left
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 6*w-84 =0
It becomes .
Result:
This is an equation! Solutions: w=14.

### Universal Simplifier and Solver

Done!

For w=14 , then 2w+3=31 and P=2(14+31)=90 which is a true statement.

Step 6. ANSWER: The width is 14 cm and the length is 31 cm.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

http://www.FreedomUniversity.TV
http://www.Twitter.com/FreedomUTVep 1. Let w be the width

Linear-equations/227731: The perimeter of a rectangle is 70 m. The length is 8 meters more than twice the width. Find the length and width.
1 solutions

Answer 169215 by drj(1380)   on 2009-10-16 22:16:39 (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 70 m. The length is 8 meters more than twice the width. Find the length and width.

Step 1. The perimeter P means adding up all the four sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let 2w+8 be the length since the length is 8 meters more than twice the width

Step 4. Then, P=w+w+2w+8+2w+8=70.

Step 5. Solving yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: w=9. Graphical form: Equation was fully solved.Text form: w+w+2w+8+2w+8=70 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( w+w+2w+8+2w+8=70 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
It becomes .

Look at .
Moved to the right of expression
It becomes .

Look at .
Eliminated similar terms ,,, replacing them with
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Moved these terms to the left
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 6*w-54 =0
It becomes .
Result:
This is an equation! Solutions: w=9.

### Universal Simplifier and Solver

Done!

For w=9 , then 2w+8=26 and P=2(9+26)=70 which is a true statement.

Step 6. ANSWER: The width is 9 meters and length is 26 meters.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

Equations/227752: Can you help me solve this equation by substitution?
8x+2y=6
4x=3-y
1 solutions

Answer 169214 by drj(1380)   on 2009-10-16 22:12:18 (Show Source):
You can put this solution on YOUR website!
Can you help me solve this equation by substitution?

8x+2y=6
4x=3-y or 4x+y=3

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 2*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

 Rectangles/227743: Find an algebraic expression. The perimeter of a rectangle, given that the length is x yards and the width is 10 yards shorter.1 solutions Answer 169213 by drj(1380)   on 2009-10-16 22:10:24 (Show Source): You can put this solution on YOUR website!Find an algebraic expression. The perimeter of a rectangle, given that the length is x yards and the width is 10 yards shorter. Step 1. Perimeter P means adding up all four sides of the rectangle. Step 2. x-10 be the width of the rectangle since the width is 10 yards shorter. Step 3. P=x+x+x-10+x-10=4x-20 Step 4. ANSWER: Perimeter P=4x-20 (in yards). I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
 Rate-of-work-word-problems/227749: A picture 8 inches long and 6 inches wide is to be enlarged so that its length will be 12 inches. What is the width in inches, of the enlarged picture? a.6 b. 3 c. 2 4. 8 5.91 solutions Answer 169212 by drj(1380)   on 2009-10-16 22:06:38 (Show Source): You can put this solution on YOUR website!A picture 8 inches long and 6 inches wide is to be enlarged so that its length will be 12 inches. What is the width in inches, of the enlarged picture? a.6 b. 3 c. 2 4. 8 5.9 Step 1. Assume the same proportions such that where w is the width of the enlarged picture Step 2. Solving Multiply by 3w/4 to both sides of the equation Step 3. ANSWER: The enlarged width is 9 inches. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
 Travel_Word_Problems/227740: if a car averages 55 mph on a certain trip, it will arrive 2 hours early. If the car averages 35 mph it will arrive 2 hours late. How many miles is the trip?1 solutions Answer 169210 by drj(1380)   on 2009-10-16 22:00:18 (Show Source): You can put this solution on YOUR website!If a car averages 55 mph on a certain trip, it will arrive 2 hours early. If the car averages 35 mph it will arrive 2 hours late. How many miles is the trip? Step 1. distance = speed * time Step 2. Let t be the time of the trip traveling on time. Step 3. Let t-2 be the time if traveling at 55 mph. Step 4. Let 55(t-2) be the distance traveling at 55 mph. Step 5. Let 35(t+2) be the distance traveling at 35 mph. Step 6. Then, 55(t-2)=35(t+2) since the distances are equal in Steps 4 and 5. Step 7. Solving the equation in Step 6 yields the following steps Add 110-35t to both sides of the equation Divide by 20 to both sides of the equation Substitute the value of t in Steps 4 or 5. We'll do both to check if distances are equal miles and miles. Step 8. The distance is 385 miles. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
Linear_Equations_And_Systems_Word_Problems/227736: I need help solving this equation:
1 solutions

Answer 169204 by drj(1380)   on 2009-10-16 21:46:19 (Show Source):
You can put this solution on YOUR website!
I need help solving this equation:

Step 1. Add to both sides of the equation.

where we simplified and arranged in descending order.

Step 2. To solve, use the quadratic equation given as

where a=1, b=9 and c=18.

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=9 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -3, -6. Here's your graph:

Step 3. ANSWER: The solutions are -3 and -6.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

Equations/227738: Can you help me solve the system?
x+2y=-12
y=20-2x
1 solutions

Answer 169200 by drj(1380)   on 2009-10-16 21:42:09 (Show Source):
You can put this solution on YOUR website!
Can you help me solve the system?

x+2y=-12
y=20-2x or 2x+y=20

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 2*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

Equations/227739: I need help solving this equation
Solve the system
2x+5y=1
-x+6y=8
1 solutions

Answer 169198 by drj(1380)   on 2009-10-16 21:40:16 (Show Source):
You can put this solution on YOUR website!
I need help solving this equation

Solve the system

2x+5y=1
-x+6y=8

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 5*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

Equations/227730: Can someone pls show me how to solve this equation using the addition/elimination process?
1.8x-2y=0.9
0.04x+0.18y=0.15
1 solutions

Answer 169197 by drj(1380)   on 2009-10-16 21:29:13 (Show Source):
You can put this solution on YOUR website!
Can someone pls show me how to solve this equation using the addition/elimination process?
1.8x-2y=0.9 Equation A
0.04x+0.18y=0.15 Equation B

Step 1. Multiply by 0.09 to Equation A to both sides of the equation

Equation A1
Equation B
Step 2. Add Equations A1 and B to eliminate the y terms.

Step 3. Divide by 0.202 to both sides of the equation

Step 4. Substitute into Equation A to solve for y.

Step 5. Add 2y-0.9 to both sides of the equation

Step 6. Divide by 2 to both sides of the equation

Step 7. ANSWER: The solution is and

As a check, use the substitution shown below which have the same results.

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving -2*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

Linear-equations/227722: 7x+7y=28
-7x+y=57
Solve by the substitution method
1 solutions

Answer 169195 by drj(1380)   on 2009-10-16 20:59:11 (Show Source):
You can put this solution on YOUR website!
7x+7y=28
-7x+y=57

Solve by the substitution method

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 7*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

 Travel_Word_Problems/227725: An airplane flew with the wind for 5 hours. The return trip against the wind took 6 hours. If the wind was blowing at 25mph. What was the rate of the plane in still the air?1 solutions Answer 169194 by drj(1380)   on 2009-10-16 20:56:54 (Show Source): You can put this solution on YOUR website!An airplane flew with the wind for 5 hours. The return trip against the wind took 6 hours. If the wind was blowing at 25mph. What was the rate of the plane in still the air? Step 1. distance= speed * time Step 2. Let x+25 be the airplane speed with the wind. Step 3. Let x-25 be the airplane speed against the wind. Step 4. Let 5(x+25) be the distance traveled with the wind after 5 hours. Step 5. Let 6(x-25) be the distance traveled again the wind after 6 hours. Step 6. Equate Steps 4 and 5 since the distances are the same. Add 150-5x to both sides of the equation Check if distances are equal: (275+25)5=(275-25)6 which is a true statement. Step 7. ANSWER: The speed of the plane is 275 miles per hour. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
 Travel_Word_Problems/227721: The speed of train A is 12 km/hr is slower than the speed of train B. Train A travels 230 km in the same time it takes train B to travel 290 km,. Find the speed of each.1 solutions Answer 169192 by drj(1380)   on 2009-10-16 20:48:35 (Show Source): You can put this solution on YOUR website!The speed of train A is 12 km/hr is slower than the speed of train B. Train A travels 230 km in the same time it takes train B to travel 290 km,. Find the speed of each. Step 1. or Step 2. Let x be the speed of train B Step 3. Let x-12 be the speed of train A since it is 12 km/hr slower. Step 4. Let be the time traveled by train A. Step 5. Let be the time traveled by train B. Step 6. Set the equations in Steps 4 and 6 since they traveled at the same time. Multiply by to both sides of the equation to get rid of the denominators. Add 3480-230x to both sides of the equation Divide by 60 to both sides of the equation speed of Train B and hours which is a true statement. Step 7. ANSWER: The speed of Train A is 46 km/hr and speed of Train B is 58 km/hr. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
 Linear-systems/227550: Why is it true that at x-intercept, the value of y is 0, and at y-intercept, the value of x is 0?1 solutions Answer 169183 by drj(1380)   on 2009-10-16 19:59:49 (Show Source): You can put this solution on YOUR website!Why is it true that at x-intercept, the value of y is 0, and at y-intercept, the value of x is 0? To answer your question, let's look at an example shown below by graphing two points since two points make a line: Equation of a line in standard form. Step 1. Let x=0 then 5y=10 or y=2. So one point is (0,2). Step 2. Let y=0 then 2x=10 or x=5. So another point is (5,0). Step 3. Now, draw a graph using these two points (0,2) and (5,0). Step 4. Note that at point (0,2) the line intersects the y-axis and at point(5,0) the line intersects the x-axis. So the y-intercept is when x=0 or at point (0,2). And the x-intercept is when y=0 or at point (5,0). I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
 Linear_Equations_And_Systems_Word_Problems/227712: eight times a number plus six less than twice the number is 341 solutions Answer 169180 by drj(1380)   on 2009-10-16 19:50:34 (Show Source): You can put this solution on YOUR website!Eight times a number plus six less than twice the number is 34. Step 1. Let n be the number. Step 2. Let 8n be eight times a number Step 3. Let 8n+2n-6 be eight times a number plus 6 less than twice the number Step 4. Then 8n+2n-6=34 since eight times a number plus six less than twice the number is 34. Step 5. Solving yields the following steps. Add 6 to both sides of the equation Divide by 10 to both sides of the equation Step 6. ANSWER: The number is 4. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
Trigonometry-basics/227714: -6-4y=-24
2x+7y=13
1 solutions

Answer 169176 by drj(1380)   on 2009-10-16 19:34:57 (Show Source):
You can put this solution on YOUR website!
-6-4y=-24 Equation A (see Step 8 if you meant -6x-4y=-24)
2x+7y=13 Equation B

Step 1. Solve for y in Equation A .

Step 2. Add 6 to both sides of the equation

Step 3. Divide by -4 to both sides of the equation

Step 4. Now substitute into .

Step 5. Subtract from both sides of the equation

Step 6. Divide by 2 to both sides of the equation

Step 8. Now, I'll assume you meant to solve the following linear system of equations

-6x-4y=-24 Equation A
2x+7y=13 Equation B

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving -4*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

I hope the above steps were helpful.