Question

Kendra was given this system of equations.

Negative 3 x + 7 y = negative 15. Negative 2 x minus 7 y = 5.

Kendra’s work is shown in the table. Where, if anywhere, did Kendra first make a mistake?

Steps
Kendra’s Work

Step 1

Negative 3 x + 7 y = negative 15. Negative 2 x minus 7 y = 5. Negative 5 x = negative 10.

Step 2

Negative 5 x = negative 10. x = 2.

Step 3

Negative 3 (2) + 7 y = negative 15. Negative 6 + 7 y = negative 15. 7 y = negative 9. y = Negative StartFraction 9 Over 7 EndFraction = negative 1 and StartFraction 2 Over 7 EndFraction

step 1
step 2
step 3
no mistake

Answer 1

To evaluate Kendra's work, we need to assess each step of her solution to the system of equations:

1. **Original equations:**
- \( -3x + 7y = -15 \)
- \( -2x - 7y = 5 \)

2. **Kendra's Step 1:**
Kendra writes:
\[ -5x = -10 \]
This implies she combined the two equations. Let's analyze this. Adding the first equation and the second:
\[
(-3x + 7y) + (-2x - 7y) = -15 + 5
\]
This simplifies to:
\[
-5x + 0y = -10 \quad \text{(correctly yielding } -5x = -10\text{)}
\]
This step is correct.

3. **Kendra's Step 2:**
Kendra states:
\[ -5x = -10 \quad \Rightarrow \quad x = 2 \]
This is also correct.

4. **Kendra's Step 3:**
Kendra substitutes \( x = 2 \) into the first equation:
\[
-3(2) + 7y = -15
\]
This simplifies to:
\[
-6 + 7y = -15
\]
Then she adds 6 to both sides:
\[
7y = -15 + 6 \quad \Rightarrow \quad 7y = -9
\]
Finally, dividing by 7 gives:
\[
y = -\frac{9}{7} \quad \text{or} \quad -1 \frac{2}{7}
\]
This is also correct.

After evaluating all steps, Kendra did not make any mistakes. Her work to solve the system of equations is accurate.

The final conclusion is **no mistake.**