# Questions on Algebra: Systems of Linear Equations answered by real tutors!

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Question 994780: Is point (4,5) part of the solution for 3x – 6y ≤ 30? Why or why not?
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Is this true or is this false?

Question 994697: A movie theater charges $8 for adults and$ 6 for seniors. On a particular day when 344 people paid an admission, the total receipts were $2575. Round your answers to the nearest integers. Answer by Boreal(1464) (Show Source): You can put this solution on YOUR website! adults=x seniors=y x+y=344 8x+6y=2575 -6x-6y= -2064, multiplying the top equation by (-6) 2x=511 x=255.5 or 256 adults y=88 seniors 256*$8=$2048 88*$6=$528$2576
===

Question 994700: An airplane travels 2310 miles in 3.5 hours with the aid of a tail wind. It takes 4 hours for the return trip, flying against the same wind. Find the speed of the airplane in the still wind, and the speed of the wind.
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Find the 2 groundspeeds, upwind and downwind.
The plane's airspeed is the average of the 2.
---
Windspeed = difference between airspeed and groundspeed.

Question 994661:
(1 pt)

Solve the given system, using the substitution method.

y = 3x – 4
9x – 3y = 14

A.

There is no solution.

B.

(12, 14)

C.

(14, 12)

D.

There are an infinite number of solutions.

You can put this solution on YOUR website!
Solve the given system, using the substitution method.
y = 3x – 4
9x – 3y = 14
----
9x-3(3x-4) = 14
-----
9x - 9x + 12 = 14
---
12 = 14
-------
Ans: No solution
-------------------
Cheers,
Stan H.

Question 994607: what is the value of x in the solution of the system?
-3x-y+2z=7
2y+z=-5
3x+6y=-21
A.-4
B.3
C.-2
D.1

You can put this solution on YOUR website!
Add the 1st and 3rd equations,

Now multiply the second equation by and add to this last equation,

So then,

Question 994564: The ordered pairs in each exercise are for the same direct variation. Find each missing value. (1,y) and (2/3,-9)
Your help is greatly appreciated! THANK YOU!

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The ordered pairs in each exercise are for the same direct variation. Find each missing value. (1,y) and (2/3,-9)
---------------
y/1 = -9/(2/3)
---
y = -27/2
---
y = -13.5
-------
Cheers,
Stan H.
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Question 994380: I have been trying to solve the following linear equation
3X-5Y=11
2x-6y=2
I keep getting the wrong answer so when I checked with you guys I noticed that it was substituted with 2(11-5y)/3-6y=2
I understand the substitution part but how do I solve from here what does the / mean next to the 3 what operation I'm suppose to there, I'm confused please help.

Found 2 solutions by rothauserc, Alan3354:
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3x -5y = 11
2x -6y = 2
************************
solve second equation for x
add 6y to both sides of =
2x = 6y + 2
divide both sides of = by 2
x = 3y + 1
************************
now substitute for x in first equation
3(3y + 1) - 5y = 11
9y + 3 - 5y = 11
4y + 3 = 11
subtract 3 from both sides of =
4y = 8
divide both sides of = by 4
y = 2
******************************************
substitute for y in first equation
3x - 5(2) = 11
3x - 10 = 11
add 10 to both sides of =
3x = 21
divide both sides of = by 3
x = 7
*****************************************
solution is x = 7 and y = 2
****************************************
check this solution by substituting the solution in the second equation
2(7) -6(2) = 2
14 - 12 = 2
2 = 2
our solution checks

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I have been trying to solve the following linear equation
3X-5Y=11
2x-6y=2 divide by 2 --> x - 3y = 1 --> x = 3y + 1
----
Sub for x in the 1st eqn
3X-5Y=11
3(3y+1) - 5y = 11
9y+3 - 5y = 11
4y = 8
y = 2
------
x = 3y + 1
x = 7

Question 994169: how do I solve 4(y - 1) + 5(y + 2) = 3(y – 8)

Question 994172: Find four solutions of each equation. Write the solutions as ordered pairs. y=12
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Find four solutions of each equation. Write the solutions as ordered pairs. y=12
----
Ans:
(1,12); (-2,12); (3,12,); (100,12)
---
Cheers
Stan H.
---------

Question 994178: Carissa makes bracelets to sell at craft fairs. The supplies she needed to start her business cost her $45. In addition, the supplies for each bracelet cost her$3. She sells her bracelets for $5. What is the minimum number of bracelets she must sell to make a profit? 2. Write an equation that Carissa could use to determine her total cost, 'C', for making 'n' bracelets 3. Write an equation she could use to find the profit, 'P', she makes from selling 'n' bracelets Answer by solver91311(20879) (Show Source): You can put this solution on YOUR website! John My calculator said it, I believe it, that settles it Question 994183: Caryssa makes bracelets to sell at craft fairs. The supplies she needed to start her business cost her$45. In addition, the supplies for each bracelet cost her $3. She sells her bracelets for$5. What is the minimum number of bracelets she must sell to make a profit.
2. Write an equation that Caryssa could use to determine her total cost, "C", for making "n" bracelets.
3. Write an equation that she could use to find the profit, "P", she makes from selling "n" bracelets.

You can put this solution on YOUR website!

John

My calculator said it, I believe it, that settles it

Question 993698: Good morning or afternoon whichever time zone you are in. I have a question about a linear equation I would like to ask. The problem is:
x=7-4y
6x-5y=-45
My question is, with the equation x=7-4y, do I add 4y to both sides of the equation so it looks like x+4y=7, before continuing to solve the rest of the problem?

You can put this solution on YOUR website!
No, you should substitute for x in the second equation with the first equation.

Then solve for y.
Then go back and use the first equation to solve for x.

Question 993634: determined the quadratic function whose graph is given. the vertex is (3,-11) and the y-intercept is -2
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given:the vertex is (,) and the y-intercept is
use vertex form of equation:
where vertex: (,) and y-intercept: (,)
so, we will use given points to find coefficient :
vertex: (,)= (,) and
the y-intercept (,)= (,)

Question 993548: What is the ordered pair for x+y=160 and x=4y+30

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.
What is the ordered pair for x+y=160 and x=4y+30?
-----------------------------------------------------

You are lucky!  You just have  x  expressed via  y:  x=4y+30.

Now substitute it into the first equation.  In this way you will exclude  x  and will obtain a single equation for  y  only:

(4y+30) + y = 160.

Simplify and solve it:

5y = 130,

y = = 26.

Now substitute the found value of  y  into the second equation of the original system to get  x:

x = 4*26 + 30 = 104 + 30 = 134.

Answer.  x = 134,  y = 26.

Question 993464: How do i solve. 2/3(k—9)= 4(k—19)
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Assuming this is

-->

-->

-->

Question 993497: What is the slope of 15x+20y=2

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The slope of a linear equation of the form is

John

My calculator said it, I believe it, that settles it

Question 993486: I.M. Rich, distributes his fortune as follows and in this order:
- The first $5 million goes to my best friend, Sam, my dog; - Half the remainder goes to my high school teacher; - Then, I give$50 million to build a new hospital in town;
- Of the remaining amount, 50% goes to my wife, 40% to my daughter, 9% to my lawyer, and 1% to my lazy son.
All the son gets is $10,000 How much was I.M. Rich's fortune? Justify your answer How much did each person receive? Answer by macston(4006) (Show Source): You can put this solution on YOUR website! . Start with the remaining amount at the end: The son's 1% of the remaining amount was$10,000,
so the remaining amount was $10000/0.01=$1,000,000.
Plus what was given to the hospital is $51,000,000. This is the other "half the remainder" The first half went to the teacher, so both halves were$102,000,000.
Add back the $5,000,000 to Sam, the total fortune was$107,000,000
.
CHECK:
From the beginning:
$107,000,000.....-$5,000,000 to Sam leaves
$102,000,000.....-$51,000,000 to teacher leaves
_$51,000,000.....-$50,000,000 for hospital leaves
.._$1,000,000.....-$500,000 wife's 50% leaves
___$500,000.....-$400,000 daughter's 40% leaves
___$100,000.....-$90,000 lawyer's 9% leaves
..___$10,000.....Lazy son's share=$10,000

Question 993366: the cost of a gym membership includes the initial fee and a monthly fee. Find the initial and monthly fees if the total cost for 5 months is $225 and the total cost for 10 months is$375.
You can put this solution on YOUR website!
.
M=monthly fee; F=initial fee
.
Total cost=initial fee+(number of months)(monthly fee)
.
$225=F+5M$225-5M=F
.
$375=F+10M$375=($225-5M)+10M$375=$225+5M$150=5M
$30=M ANSWER 1: The monthly fee is$30.
.
$225=F+5M$225=F+5($30)$225=F+$150$75=F
ANSWER 2: The initial fee is $75 . CHECK:$375=F+10M
$375=$75+10($30)$375=$75+$300
$375=$375

Question 992946: What is the slope of 2y+1=0?
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x is unrestricted and .
No vertical change. What is the slope!

Find a slope-intercept form equation for the line Through (3,3) with slope of -2/5

Found 2 solutions by jim_thompson5910, MathLover1:
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Point Slope form

Plug in the given slope

Plug in the given point

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a slope-intercept form equation for the line is
where is a slope and is y-intercept
given: the line passes through (,) and has slope of
so far we have
now use given point (,) to find

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Distribute 2 across the binomial factor in the LHS. Collect like terms. Add the additive inverse of the constant term in the LHS to both sides of the equation. Multiply both sides of the equation by the reciprocal of the coefficient on the variable.

John

My calculator said it, I believe it, that settles it

Question 992405: x+y=k
x-y=k
the solution to the system shown is
(0,k)
(2,2)
(k,0)

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x+y=k
x-y=k
-----
2x = 2k
x = k
----
Solve for "y"
k + y =k
y = 0
-----
Solution: (k,0)
Cheers,
Stan H.
---------------

the solution to the system shown is
(0,k)
(2,2)
(k,0)

Question 992311: 3X + y = 1
5x + y = 1

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Hi dear
Call 3x+y=1-----(1)
and 5x+y=1-----(2)
subtract equ 1 from equ 2
2x=0
x=0
put x=0 in equ 1
y=1

3/2x + 1/5= 3/4
My LCD is 20.
Thank you

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.
The equation is ambiguous.
Always use parentheses to clarify equations.
.
Is the equation:

=
.
Or is the equation:

=

Question 991842: The diameter of a sphere is reduced by 10%. By what percent will the volume be reduced?
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since diameter = 2 times the radius, then if you reduce the diameter by 10%, you also reduce the radius by 10%.

for example:

assume the diameter is 10.
reduce it by 10% and the diameter is now 9.

since the diameter is 10, the radius has to be 10/2 = 5.
since the reduced diameter is 9, the reduced radius has to be 9/2 = 4.5.

5 - 4.5 is equal to .5 and .5 / 5 is equal to .10 which is equal to 10%, so the radius has been reduced by 10% as well.

the formula for the volume of a sphere is 4/3 * pi * r^3.

this is because r - .10 * r is equal to r * (1 - .10) which is equal to r * .9.

reduce the radius by 10% and the formula becomes v = 4/3 * pi * (.9*r)^3 which becomes v = 4/3 * pi * .9^3 * r^3 which then becomes v = 4/3 * pi * .729 * r^3.

this can be rewritten as v = .729 * 4/3 * pi * r^3.

the volume has been reduced by (1 - .729) = .271, or 27.1%.

let's take an example:

assume the diameter of the sphere is 24 inches.

the radius then has to be 12 inches because the length of the radius is half the length of the diameter.

the volume of the sphere is 4/3 * pi * 12^3 which is equal to 4/3 * pi * 1728.

reduce the diameter by 10%.

24 - .10 * 24 = 24 - 2.4 = 21.6

this is the same as .9 * 24 which is equal to 21.6.

this is because 24 - .10 * 24 is equal to 24 * (1 - .10) which is equal to .9 * 24.

the radius of this sphere is equal to 21.6 / 2 = 10.8

the volume of this sphere is equal to 4/3 * pi * (10.8)^3 which is equal to 4/3 * pi * 1259.712.

the volume of the original sphere is 4/3 * pi * 1728.

the volume of the reduce sphere is 4/3 * pi * 1259.712.

the difference in the volume is 4/3 * pi * 1728 - 4/3 * pi * 1259.712.

this can be rewritten as 4/3 * pi * (1728 - 1259.712) which can then be simplified to 4/3 * pi * 468.288.

the ratio of this difference to the original volume is:

(4/3 * pi * 468.288) / (4/3 * pi * 1728).

4/3 * pi / 4/3 * pi cancels out because it is equal to 1 and you are left with:

the ratio of the difference is equal to 468.288 / 1728 which is equal to .271 which is equal to 27.1%.

reduce the diameter of the sphere by 10% and you reduce the volume of the sphere by 27.1%.

Question 991747: Is 55y=8x+25 a equation?
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It has an equal sign.
It's an equation.

Question 991488: The Community College basketball team made 51 field goals in a game, some were 2 pointers, and some were 3 pointers. They score 130 points. How many 2 point and 3 point baskets were made?
You can put this solution on YOUR website!
.
x=number of two point goals; y=number of three point goals
.
x+y=51
y=51-x
.
2x+3y=130
2x+3(51-x)=130
2x+153-3x=130
153-x=130
23=x
.
y=51-x=51-23=28
.
CHECK:
2x+3y=130
2(23)+3(28)=130
46+84=130
130=130

Question 991371: What is the value of x and z when given the following degrees: (8x-3), 77 and z
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What is the relationship between the angles?

Question 991496: Solve by elimination
2x-4y-z=8
3x+2y+z=6
5x-2y+3z=3

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Add the first two equations to eliminate z. Then add the result to the third equation and get the absurdity 0 = 17. The system is inconsistent.

John

My calculator said it, I believe it, that settles it

Question 991350: 7x – 4y = –7
5x + y = 22

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.
.
5x+y=22
y=22-5x
.
7x–4y=–7
7x-4(22-5x)=-7
7x-88+20x=-7
27x=81
x=3
.
5x+y=22
5(3)+y=22
15+y=22
y=7
.

Question 991058: A gym charges a one time joining fee of $50 and then a monthly membership fee of$25.
Write a function to represent the situation and define the variables.

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It's a "today only" deal, right?

x-3y=1

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.
.

Express  x  from the second equation,  x = 3y+1,  and substitute it into the first equation.  You will get the equation for a single unknown  y:

3*(3y + 1) + 2y = 25.

Simplify and solve it:

9y + 3 + 2y = 25,

11y = 25 -3,

11y = 22.

4x+2y=12

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.
.

Simply substitute the expression for  y  from the first equation to the second one.  You will get

4x + 2*(-2x+3) = 12.

Simplify it:

4x - 4x + 6 = 12.

6 = 12.

Could it be so?   -No.

It means that your system has no solution.

Geometrically the original equations represent two parallel straight lines in a coordinate plane that have no intersection - have no common point.

Question 990987: Is 9x+11zy=12y linear? And write it in standard form
Answer by Edwin McCravy(13211)   (Show Source):
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9x+11zy = 12y

No, that's not linear because it is of degree 2 since it has a term
in which 2 letters are multiplied together, z and y.

A linear equation can have no letters multiplied together such as x2, xy, etc.

In standard form it is solved for y:

9x+11zy = 12y

9x = 12y-11zy

9x = y(12-11z)

Edwin

-2x+2y=-16

You can put this solution on YOUR website!
Already set for elimination of x to first find y.
Add the corresponding members to start.

Question 990636: can you help me solve this please thanks?
x+y-z=0
2x-y+z=3
-x+5y-3z=2

You can put this solution on YOUR website!

Since you didn't specify a method, here is Gauss-Jordan row reduction.
 1    1    -1    0
2   -1     1    3
-1    5    -3    2

1    1    -1    0    -2R1 + R2 to R2
0   -3     3    3
-1    5    -3    2

1    1    -1    0    -R1 + R3 to R3
0   -3     3    3
0    6    -4    2

1    1    -1    0    -R2/3 to R2
0    1    -1   -1
0    6    -4    2

1    1    -1    0    -6R2 + R3 to R3
0    1    -1   -1
0    0     2    8

1    1    -1    0    R3/2 to R3
0    1    -1   -1
0    0     1    4

1    1     0    4    R3 + R1 to R1
0    1    -1   -1
0    0     1    4

1    1     0    4    -R2 + R1 to R1
0    1     0    3
0    0     1    4

1    0     0    1    R3 + R2 to R2
0    1     0    3
0    0     1    4


John

My calculator said it, I believe it, that settles it

Question 990672: Suppose a devastating freeze destroyed roughly 85% of California Central Valley's orange crop. As a result of the freeze, an orange that cost $0.50 before the freeze would cost$1.50 after the freeze. Model the price c of an orange as a linear function of the percentage p of the crop that was destroyed. (Hint: When 0% of the crop was destroyed, the price was \$0.50.)
You can put this solution on YOUR website!
You want ordered pair points as (percentDamaged,price). Two points you have are (0,0.5) and (85,1.5), which you may assign coordinate variables as (p,c).

Notice that one of these points is the c-axis intercept! Feed everything into slope-intercept form and simplify:

Question 990739: How do you simplify the quadratic 3x^2+3x-6=0 into 2 binomials?
Found 2 solutions by MathLover1, Boreal:
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.......all terms divide by
......factor

=> product of binomials

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3x^2+3x-6=0
3(x^2+x-2)=0
3(x+2)(x-1)=0
x= -2, 1

Question 990655: If X+y+z=112 and y=4x and z=11y then find the value of y
You can put this solution on YOUR website!
.
You are given

x + y + z = 112,
y = 4x,
z = 11y.

Find y.
---------------------------------------

Substitute  y = 4x  and  z = 11y = 11*(4x) = 44x  into the first equation.  You will have

x + 4x + 44x = 112,     or

49x = 112.

Hence,  x = .

Therefore,  y = 4x = = .

Question 990423: 3, 5 is on the graph of 3x + 5 y equals 30 tell whether the statement is true or false and justify your answer
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Fastest way is to substitute.
3(3)+5(5)=9+25=34
It is false.

Question 990347: Describe two applications for graphing linear equations

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Would you narrow that a bit? Too too many applications. Check in your textbook about applications, included with many exercise sets and often in separate Applications sections of the books.

A very common academic exercise is ticket sales, numbers of types of tickets, and the revenue.

Question 990022: Make up a pair of linear equations with solution: x = 6 and y = 10.
You can put this solution on YOUR website!
Make up a pair of linear equations with solution: x = 6 and y = 10.
---
2x = 12
3y = 30
---
1st Equation: 3y+2x = 42
---------
-5x = -30
2y = 20
---
2nd Equation:: 2y-5x = -10
------------
Cheers,
Stan H.
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