Question

Solve the following system of equations using substitution and show all work.

Answer 1

2x + y = 20

y = 20 - 2x

Substitute into second equation:

6x - 5(20-2x) = 12

6x -100 +10x = 12

16x = 112

x = 7

Plug back into first equation:

2(7) + y = 20

14 +y = 20

y = 6

Answer is x = 7 and y = 6

Answer 2

2x + y = 20

6x - 5y = 20

2x + y = 20

Subtract 2x on both sides to get "y" by itself, so you can later substitute it into the second equation.

2x + y - 2x = 20 - 2x

y = 20 - 2x

6x - 5y = 12

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

6x - 100 + 10x = 12    Combine like terms

16x - 100 = 12     Add 100 on both sides  

16x - 100 + 100 = 12 + 100

16x = 112    Divide 16 on both sides to get "x" by itself

x = 7

Plug in x into either of the original equations to find y.

2x + y = 20

2(7) + y = 20

14 + y = 20

y = 6

x = 7, y = 6