Question

Put the steps in order that are used to solve the following systems of equations by substitution. −7x−2y=−13 x−2y=11

Answer 1

1. Solve one of the equations for one variable in terms of the other variable. In this case, solve the second equation for x in terms of y: x = 2y + 11.
2. Substitute the expression found in step 1 into the other equation. Replace x in the first equation with (2y + 11): -7(2y + 11) - 2y = -13.
3. Solve the resulting equation for the remaining variable. Distribute the -7 to the terms inside the parentheses: -14y - 77 - 2y = -13. Combine like terms: -16y - 77 = -13.
4. Solve for y by isolating the variable. Add 77 to both sides: -16y = 64. Divide both sides by -16: y = -4.
5. Substitute the value of y into one of the original equations to solve for x. Use the second equation: x - 2(-4) = 11. Simplify: x + 8 = 11. Subtract 8 from both sides: x = 3.
6. Verify the solution by substituting the values of x and y into the other equation: -7(3) - 2(-4) = -13. Simplify: -21 + 8 = -13. The equation is true.
7. The solution to the system of equations is x = 3, y = -4.