Question

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

• -7(2y+11)-2y=-13

• x+8=11

• x - 2y = 11 —> x = 2y + 11

• -16y - 77 = -13

• x = 3

• -14y - 17 -2y = -13

• y = -4

• -16y = 64

• x - 2 (-4) = 11

• (3,-4)

Answer 1

1. Rearrange one of the equations to solve for one variable in terms of the other variable. In this case, we rearrange the second equation to solve for x in terms of y: x = 2y + 11.
2. Substitute the value of x from the rearranged equation into the other equation. Replace x in the first equation with 2y + 11: 7(2y + 11) - 2y = -13.
3. Simplify the equation from step 2. Expand and combine like terms: 14y + 77 - 2y = -13.
4. Solve for y. Combine like terms and isolate the y-term: 12y + 77 = -13. Then, subtract 77 from both sides: 12y = -90. Finally, divide both sides by 12: y = -4.
5. Substitute the value of y back into one of the original equations to solve for x. Replace y in the second equation with -4: x - 2(-4) = 11. Simplify and solve for x: x + 8 = 11, x = 3.
6. Write the solution as an ordered pair (x, y). The solution to the system of equations is (3, -4).