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

−7x−2y=−13


x−2y=11


(10 points)
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1 answer

To solve the system of equations by substitution, follow the steps below in the correct order:

  1. Choose one of the equations to solve for one variable.

    • For example, you can solve the second equation \( x - 2y = 11 \) for \( x \).

  2. Rearrange the chosen equation to isolate one variable.

    • From \( x - 2y = 11 \), you can isolate \( x \) to get \( x = 2y + 11 \).

  3. Substitute the expression found in step 2 into the other equation.

    • Substitute \( x \) in the first equation \( -7x - 2y = -13 \) with \( 2y + 11 \).

  4. Solve the resulting equation for the remaining variable.

    • You would solve the equation \( -7(2y + 11) - 2y = -13 \).

  5. Back-substitute to find the value of the first variable.

    • Once you have the value of \( y \), substitute it back into the equation from step 2 to find \( x \).

  6. State the solution as an ordered pair.

    • Write the solution as \( (x, y) \).

This outlines the general steps for solving the system of equations by substitution.