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Solve using substitution: -y - 5x = -7 2y - 2x = 14

im a senior in high school and doing credit recovery and need help with math a lot.

TINA H. | Multi-Subject TutorMulti-Subject Tutor
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First, solve one of the equations for one of the expressions:

-y -5x   =      -7
+5x       +5x

-y = 5x - 7

y = -5x + 7

Then, substitue this for y in the other equation:

2(-5x + 7) -2x = 14
-10x +14 - 2x = 14
-12x +14 = 14
-14     -14
-12x  =  0
-12        -12
x    =  0

Then, solve the other equation by substituting this value for x.
y = -5x + 7
y = -5(0) +7
y = 0 + 7
y = 7

-y-5x=-7  Solve where x=0 and y=7
-7 -5(0) = -7
-7-0=-7
-7 = -7

2y-2x=14 Solve where x=0 and y=7
2(7) -2(0) = 14
14-0=14
14=14

George T. | George T.--"It's All About Math!"George T.--"It's All About Math!"
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Sean

Lets label the two equations as A) and B):

A) -y-5x=-7
B) 2y-2x=14

First, we can solve equation A) for y, as follows:

Add 5x to both sides:  -y=-7+5X
Multiply both sides by -1:  y=7-5x

Next we can substitute this result for y into equation B), simplify, and solve for x as follows:

B) 2(7-5x)-2x=14
14-10x-2x=14
14-12x=14
-12x=14-14
-12x=0
x=0  We have now solved for x.

Finally, we can plug 0 in for the value of x in either equation, to solve for y.  Let's use equation A):

A) -y-5x=-7
-y-(5)(0)=-7
-y=-7
y=7  We have now solved for y.

We can check this result by substituting the values for x and y (0 and 7) back into each equation A) and B) to ensure that the values work.  This can be left to the student.

Hope this helps!

George T.