Put the steps in order that are used to solve the following systems of equations by substitution.%0D%0A%0D%0A−7x−2y=−13%0D%0A−%0D%0A7%0D%0A𝑥%0D%0A−%0D%0A2%0D%0A𝑦%0D%0A=%0D%0A−%0D%0A13%0D%0A%0D%0Ax−2y=11

Answer 1

To solve the system of equations using substitution, follow these steps, putting them in the correct order:

1. Choose one of the equations to solve for one variable. For instance, you can solve the second equation \( x - 2y = 11 \) for \( x \): \[ x = 2y + 11 \]

2. Substitute this expression into the other equation. Now, substitute \( x = 2y + 11 \) into the first equation \( -7x - 2y = -13 \): \[ -7(2y + 11) - 2y = -13 \]

3. Simplify and solve for the remaining variable. Distribute and combine like terms: \[ -14y - 77 - 2y = -13 \ -16y - 77 = -13 \ -16y = 64 \ y = -4 \]

4. Substitute back to find the other variable. Use the value of \( y \) found in step 3 and substitute it back into the equation from step 1 to find \( x \): \[ x = 2(-4) + 11 \ x = -8 + 11 \ x = 3 \]

5. Combine the results into a solution. The solution to the system of equations is: \[ (x, y) = (3, -4) \]

So the ordered steps to solve the system of equations by substitution are:

1. Solve one of the equations for one variable.
2. Substitute that expression into the other equation.
3. Simplify and solve for the remaining variable.
4. Substitute back to find the other variable.
5. Combine the results into a solution.