Put the steps in order that are used to solve the following systems of equations by substitution.

Question

−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.