Question

Put the steps in order that are used to solve the following systems of equations by substitution.

-7x - 2y = - 13
x - 2y = 11


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

Answer 1

To solve the system of equations using substitution, the steps should be ordered logically. Here’s the correct sequence based on your provided equations:

1. **Start with the original equations:**
\(-7x - 2y = -13\)
\(x - 2y = 11\)

2. **Solve for x in terms of y from the second equation:**
\(x - 2y = 11 \implies x = 2y + 11\)

3. **Substitute the expression for x into the first equation:**
\(-7(2y + 11) - 2y = -13\)

4. **Distribute and simplify:**
\(-14y - 77 - 2y = -13\)
Combine like terms:
\(-16y - 77 = -13\)

5. **Solve for y:**
\(-16y = 64 \implies y = -4\)

6. **Substitute back to find x:**
\(x = 2(-4) + 11 \implies x = 3\)

7. **State the solution:**
The solution to the system is \((3, -4)\).

Putting everything together, the ordered steps are as follows:

1. \(x - 2y = 11 \rightarrow x = 2y + 11\)
2. \(-7(2y + 11) - 2y = -13\)
3. \(-14y - 77 - 2y = -13\)
4. \(-16y - 77 = -13\)
5. \(-16y = 64 \rightarrow y = -4\)
6. \(x = 2(-4) + 11 \rightarrow x = 3\)
7. \((3, -4)\)

This is the correct order of steps to solve the system of equations using substitution.