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

To solve the system of equations -7x - 2y = -13 and x - 2y = 11 by substitution, the following steps are used:

1. Start with one of the equations and solve for one variable in terms of the other.
x - 2y = 11 (Equation 2)
x = 2y + 11

2. Substitute the expression for the variable from step 1 into the other equation.
-7(2y + 11) - 2y = -13
-14y - 77 - 2y = -13

3. Simplify the equation from step 2 by combining like terms.
-16y - 77 = -13

4. Solve the resulting equation from step 3 for the remaining variable.
-16y = -13 + 77
-16y = 64
y = 64 / -16
y = -4

5. Substitute the value of y into one of the original equations to solve for x.
x - 2(-4) = 11
x + 8 = 11
x = 11 - 8
x = 3

6. The solution to the system of equations is (x, y) = (3, -4).