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

Answer 1

To solve the system of equations

\[
-7x - 2y = -13
\]

\[
x - 2y = 11
\]

by substitution, let's put the provided steps in the correct order:

1. Solve one of the equations for one variable. Here, we can rearrange the second equation:

\( x - 2y = 11 \)

to isolate \( x \):

\[
x = 2y + 11
\]

2. Substitute this expression for \( x \) into the first equation:

\[
-7(2y + 11) - 2y = -13
\]

3. Expand and simplify the equation:

\[
-14y - 77 - 2y = -13
\]

Combine like terms:

\[
-16y - 77 = -13
\]

4. Solve for \( y \):

Add 77 to both sides:

\[
-16y = 64
\]

Then divide by -16:

\[
y = -4
\]

5. Substitute \( y = -4 \) back into the equation we derived for \( x \):

\[
x = 2(-4) + 11
\]
Simplifying gives:

\[
x = -8 + 11 = 3
\]

6. The solution is \( (3, -4) \).

Putting it all together, the correct order of steps is:

1. \( x - 2y = 11 \) → \( x = 2y + 11 \)
2. Substitute into the first equation: \( -7(2y + 11) - 2y = -13 \)
3. Expand: \( -14y - 77 - 2y = -13 \)
4. Combine: \( -16y - 77 = -13 \)
5. Solve for \( y \): \( -16y = 64 \) → \( y = -4 \)
6. Substitute \( y = -4 \) into \( x = 2y + 11 \) → \( x = 3 \)
7. Solution is \( (3, -4) \)