Question 258303: Sloving a system of Linear equation find the value of x and y. can someone please show me the steps I need to be able to capture the information. Thanking you in advance,.
-7x -6y = 10
3x - 2y = 14?
Answer by jmorgan22(8)   (Show Source):
You can put this solution on YOUR website! I solved this in the long way to help you understand Solving Linear Equations by Substitution. I hope this helps. Have a great day.
-7x-6y=10
3x-2y=14
Since -6y does not contain the variable to solve for, move it to the right-hand side of the equation by adding 6y to both sides.
-7x=6y+10
3x-2y=14
Divide each term in the equation by -7.
-7x/-7=6y/-7+10/-7
3x-2y=14
Simplify the left-hand side of the equation by canceling the common factors.
x=6y/-7+10/-7
3x-2y=14
Simplify the right-hand side of the equation by simplifying each term.
x=-6y-10/7
3x-2y=14
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is (-6y-10)/7
x=-6y-10/7
3(-6y-10/7)-2y=14
Remove the parentheses around the expression -6y-10.
x=-6y-10/7
3(-6y-10/7)-2y=14
Divide each term in the numerator by the denominator.
x=-6y/7 – 10/7
3(-6y-10/7)-2y=14
Remove the parentheses around the expression -6y-10.
x=-6y/7 – 10/7
3(-6y-10/7) – 2y=14
Divide each term in the numerator by the denominator.
x=-6y/7 – 10/7
3(-6y/7 – 10/7) – 2y = 14
Combine the numerators of all expressions that have common denominators.
x=-6y/7 – 10/7
3(-6y – 10/7) – 2y=14
Multiply 3 by each term inside the parentheses.
x=-6y/7 – 10/7
- 6(3y+5)/7 – 2y = 14
Multiply -6 by each term inside the parentheses.
x=-6y/7 – 10/7
-18y – 30/7 – 2y = 14
Divide each term in the numerator by the denominator.
x=-6y/7 – 10/7
-18y/7 – 30/7 – 2y = 14
Combine the numerators of all expressions that have common denominators.
x=-6y/7 – 10/7
-18y -30/7 – 2y = 14
Factor out the GCF of -6 from each term in the polynomial.
x=-6y/7 – 10/7
-6(3y) -6(5)/7 – 2y = 14
Factor out the GCF of -6 from -18y-30.
x=-6y/7 – 10/7
-6(3y+5)/7 – 2y = 14
Move the -1 to the front of the fraction.
x=-6y/7 – 10/7
- 6(3y+5)/7 – 2y = 14
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 7.
x=-6y/7 – 10/7
- 6(3y+5)/7 -2y* 7/7 = 14
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 7.
x=-6y/7 – 10/7
- 6(3y+5)/7 – 2y*7/7 = 14
Multiply 2y by 7 to get 14y.
x=-6y/7 – 10/7
- 6(3y+5)/7 – 14y/7 = 14
The numerators of expressions that have equal denominators can be combined. In this case,- 6(3y+5)/7 and – (14y/7) have the same denominator of 7, so the numerators can be combined.
x=-6y/7 – 10/7
-6(3y+5) – (14y)/7 =14
Simplify the numerator of the expression.
x=-6y/7 – 10/7
-18y-30-14y/7 = 14
Since -18y and -14y are like terms, subtract 14y from -18y to get -32y.
x=-6y/7 – 10/7
-32y-30/7 = 14
Factor out the GCF of -2 from each term in the polynomial.
x=-6y/7 – 10/7
-2(16y) – 2(15)/7 = 14
Factor out the GCF of -2 from -32y-30.
x=-6y/7 – 10/7
-2(16y+15)/7 = 14
Remove the parentheses from the numerator.
x=-6y/7 – 10/7
- 2(16y+15)/7 = 14
Multiply each term in the equation by 7.
x=-6y/7 – 10/7
- 2(16y+15)/7 * 7=14* 7
Simplify the left-hand side of the equation by canceling the common factors and Multiply 14 by 7 to get 98..
x=-6y/7 – 10/7
-2(16y+15)=98
Divide each term in the equation by 2.
x=-6y/7 – 10/7
- 2(16y+15)/2 = 98/2
Simplify the left-hand side of the equation by canceling the common factors.
x=-6y/7 – 10/7
-(16y+15)=49
Multiply -1 by each term inside the parentheses.
x=-6y/7 – 10/7
-16y-15=49
Since -15 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 15 to both sides.
x=-6y/7 – 10/7
-16y=15+49
Add 49 to 15 to get 64.
x=-6y/7 – 10/7
-16y=64
Divide each term in the equation by -16.
x=-6y/7 – 10/7
-16y/-16 =64/-16
Simplify the left-hand side of the equation by canceling the common factors.
x= -6y/7 – 10/
y = - 4
Simplify the right-hand side of the equation by simplifying each term.
x = -6y/7 – 10/7
y =- 4
|
|
|
