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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 these steps in order:

  1. Select one equation to solve for one variable: Choose one of the equations and isolate one variable in terms of the other. For example, from the second equation \(x - 2y = 11\), you can solve for \(x\):

    \[ x = 2y + 11 \]

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

    \[ -7(2y + 11) - 2y = -13 \]

  3. Solve for the remaining variable: Simplify and solve the resulting equation for the remaining variable \(y\):

    \[ -14y - 77 - 2y = -13 \] \[ -16y - 77 = -13 \] \[ -16y = 64 \] \[ y = -4 \]

  4. Substitute back to find the other variable: Once you have the value of \(y\), substitute it back into the equation used in step 1 to find \(x\):

    \[ x = 2(-4) + 11 \] \[ x = -8 + 11 \] \[ x = 3 \]

  5. Write the solution: Present the solution as an ordered pair \((x, y)\):

    \[ (3, -4) \]

So, the ordered steps are:

  1. Solve one equation for one variable.
  2. Substitute that expression into the other equation.
  3. Solve for the remaining variable.
  4. Substitute back to find the other variable.
  5. Write the solution.