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

Question

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

Answer 1

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

 

Now check your work:

-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

 

 

Answer 2

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.