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

To solve the given system of equations by substitution, follow these ordered steps:

1. **Solve one of the equations for one variable**: Choose one equation and isolate one variable. For example, from the second equation, \( x - 2y = 11 \):
\[
x = 11 + 2y
\]

2. **Substitute the expression into the other equation**: Take the expression for \( x \) from step 1 and substitute it into the first equation:
\[
-7(11 + 2y) - 2y = -13
\]

3. **Solve the resulting equation**: Simplify and solve for \( y \):
\[
-77 - 14y - 2y = -13 \\
-16y - 77 = -13 \\
-16y = 64 \\
y = -4
\]

4. **Substitute back to find the other variable**: Substitute the value of \( y \) into the expression for \( x \):
\[
x = 11 + 2(-4) \\
x = 11 - 8 \\
x = 3
\]

5. **Write the solution**: The solution to the system of equations is \( (x, y) = (3, -4) \).

By following these steps, you solve the system of equations by substitution methodically.