Question

Julio tested the point (4, –2) to see whether it is a solution to this system of equations.

–3x – 2y = –8,
y = 2x – 5

His work is shown below.

Negative 3 (4) minus 2 (negative 2) = negative 8. Negative 12 + 4 = negative 8. Negative 8 = negative 8. Therefore, (4, negative 2) is a solution to the system.

Did Julio verify the solution?
No. He substituted 4 and –2 for the wrong variables.
No. He did not check the point in the second equation.
No. He simplified the equation incorrectly.
Yes. He verified that (4, –2) is a solution to the system of equations.

Answer 1

To determine whether Julio verified the solution correctly, we need to check if the point \( (4, -2) \) satisfies both equations in the system:

1. **First equation:** \( -3x - 2y = -8 \)

Substituting \( x = 4 \) and \( y = -2 \):

\[
-3(4) - 2(-2) = -8
\]
\[
-12 + 4 = -8
\]
\[
-8 = -8
\]

This is correct.

2. **Second equation:** \( y = 2x - 5 \)

Substituting \( x = 4 \) and \( y = -2 \):

\[
-2 = 2(4) - 5
\]
\[
-2 = 8 - 5
\]
\[
-2 = 3
\]

This is not correct.

Julio only checked the first equation and did not verify the point in the second equation. Therefore, the correct answer is:

**No. He did not check the point in the second equation.**