1. Solve one of the equations for one variable in terms of the other variable. In this case, let's solve the second equation for x: x = 2y + 11.
2. Substitute the expression for x from step 1 into the other equation. Replace x in the first equation with (2y + 11): -7(2y + 11) - 2y = -13.
3. Simplify and solve the resulting equation for the remaining variable. Distribute the -7: -14y - 77 - 2y = -13. Combine like terms: -16y - 77 = -13. Add 77 to both sides: -16y = 64. Divide both sides by -16: y = -4.
4. Substitute the value of y from step 3 into the expression for x from step 1 to find the value of x. Replace y in the equation x = 2y + 11 with -4: x = 2(-4) + 11. Simplify: x = -8 + 11 = 3.
5. The solution to the system of equations is x = 3 and y = -4.
Put the steps in order that are used to solve the following systems of equations by substitution.
-7x-2y=-13
x-2y=11
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