Question

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

| x-2y=11-->x=2y+11, -16y=64, x+8=11, -14y-77-2y=-13, -7(2y+11)-2y=-13, x-2(-4)=11, x=3, y=-4, -16y-77=-13, (3,-4).

Answer 1

1. Solve one of the equations for one variable in terms of the other variable. In this case, we solve the second equation for x: x = 2y + 11.
2. Substitute the expression found in step 1 into the other equation. Substitute x = 2y + 11 into the first equation: -7(2y + 11) - 2y = -13.
3. Simplify the resulting equation and solve for y. -14y - 77 - 2y = -13. Combine like terms: -16y - 77 = -13.
4. Solve the equation obtained in step 3 for y. -16y - 77 = -13. Add 77 to both sides: -16y = 64. Divide both sides by -16: y = -4.
5. Substitute the value of y obtained in step 4 into any of the original equations to solve for x. Using the second equation: x - 2(-4) = 11. Simplify: x + 8 = 11.
6. Solve the equation obtained in step 5 for x. Subtract 8 from both sides: x = 3.
7. Write the solution as an ordered pair (x, y). The solution is (3, -4).