put the steps in order that are used to solve the following systems of equations by substitution.
-7x-2y=-13
x-2y=11
To solve the system of equations by substitution, follow these steps:
1. Solve one of the equations for one variable in terms of the other variable. Let's choose the second equation and solve for "x":
x - 2y = 11
x = 2y + 11
2. Substitute the expression for the solved variable into the other equation. Let's replace "x" in the first equation with "2y + 11":
-7(2y + 11) - 2y = -13
3. Simplify the equation by distributing and combining like terms:
-14y - 77 - 2y = -13
-16y - 77 = -13
4. Solve the resulting equation for the remaining variable. Let's solve for "y":
-16y - 77 = -13
-16y = 64
y = -4
5. Substitute the value found for "y" back into one of the original equations to solve for the other variable. Let's substitute "-4" for "y" in the second equation:
x - 2(-4) = 11
x + 8 = 11
x = 3
6. Check the solution by substituting the values of "x" and "y" into the original equations. This step ensures that the solution is correct.
Therefore, the solution to the system of equations is x = 3 and y = -4.