Question

Put the steps in order that are used to solve the following systems of equations by substitution
-7x-2y=-13
x-2y=11

Answer 1

1) Solve one of the equations for one of the variables. In this case, we can solve the second equation for x by adding 2y to both sides:
x = 11 + 2y

2) Substitute the expression for the solved variable into the other equation. In this case, substitute x = 11 + 2y into the first equation:
-7(11 + 2y) - 2y = -13

3) Simplify and solve the resulting equation for the remaining variable. Distribute the -7 through the parentheses:
-77 - 14y - 2y = -13
Combine like terms:
-16y - 77 = -13
Add 77 to both sides:
-16y = 64
Divide by -16:
y = -4

4) Substitute the value of the solved variable back into the expression for the other variable. In this case, substitute y = -4 into the equation x = 11 + 2y:
x = 11 + 2(-4)
Simplify:
x = 11 - 8
x = 3

The solution to the system of equations is x = 3 and y = -4.