Question

What is the solution for the system of equations? Use the substitution method to solve. 2x+y=20

Answer 1

2x + y = 20

-5y = -6x + 12

To use the substitution method, first isolate one of the variables in one of the equations.

Isolate the "y" in the first equation (because it is the easiest to isolate), and substitute it into the second equation:

2x + y = 20     Subtract 2x on both sides

y = 20 - 2x

-5y = -6x + 12   (since y = 20 - 2x, you can substitute 20 - 2x into y)

-5(20 - 2x) = -6x + 12       Multiply -5 into (20 - 2x)

-100 + 10x = -6x +12      Add 100 on both sides

10x = -6x + 112        Add 6x on both sides

16x = 112           Divide 16 on both sides

x = 7

Now that you have found x, you can substitute 7 into x for one of the original equations:

2x + y = 20

2(7) + y = 20

14 + y = 20    Subtract 14 on both sides

y = 6

-5y = -6x + 12

-5y = -6(7) + 12

-5y = -42 + 12

-5y = -30       Divide -5 on both sides

y = 6

x = 7, y = 6