Kendra was given this system of equations.

Question

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.