Solve the system of equations -3x+7y=-18 and 4x-4y=8 by combining the equations

(-4, -3)

Step-by-step explanation:

Using elimination by addition and subtraction works best here.

Suppose we decide to eliminate x temporarily.  To do this, we multipy the first row by 4, obtaining

-12x + 28y = -72

  4x  - 4y   =   8

Next, multiply the second row by 3, obtaining the "equivalent system"

-12x + 28y = -72

  12x - 12y   =  24

Combining these equations, column by column, we get:

16y = -48.  So y = -3.

Now let's find x.  Substitute -3 for y in the second equation:

4x - 4(-3) = 8, or

4x + 12    = 8, or

4x            = 8 - 12  = -4.  This tells us that x = -4.

The solution is thus (-4, -3).