Question

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

= -16y=64
= x = 3
= −7(2y+11) - 2y = -13
= -14y-77 - 2y = -13
=-16y77 = −13
= x - 2(-4) = 11
= x+8= 11
= y = −4
= x − 2y = 11 --> x = 2y + 11
= (3,-4)

Answer 1

To solve the given system of equations using substitution, the steps can be arranged in the following order:

1. Write one equation in terms of one variable.
\[ x - 2y = 11 \rightarrow x = 2y + 11 \]

2. Substitute the expression from step 1 into the other equation.
\[ -7(2y + 11) - 2y = -13 \]

3. Distribute and combine like terms.
\[ -14y - 77 - 2y = -13 \]

4. Simplify the equation.
\[ -16y - 77 = -13 \]

5. Isolate the variable \( y \).
\[ -16y = 64 \]
\[ y = -4 \]

6. Substitute the value of \( y \) back into the equation obtained in step 1 to find \( x \).
\[ x = 2(-4) + 11 \]

7. Simplify to find \( x \).
\[ x = -8 + 11 \]
\[ x = 3 \]

8. Write the solution as an ordered pair.
\[ (x, y) = (3, -4) \]

So, the final ordered list of steps is:

1. \( x - 2y = 11 \rightarrow x = 2y + 11 \)
2. \( -7(2y + 11) - 2y = -13 \)
3. \( -14y - 77 - 2y = -13 \)
4. \( -16y - 77 = -13 \)
5. \( -16y = 64 \)
6. \( y = -4 \)
7. \( x = 2(-4) + 11 \)
8. \( x = 3 \)
9. \( (3, -4) \)