Question

Roxanne graphed this system of equations to find the solution.
y =
2
3
x − 5 y = −2x + 3
On a coordinate plane, 2 lines intersect at (negative 3, negative 3).
She determined that the solution is (–3, –3). Is she correct? If not, explain why.
Yes, she is correct.
No. She switched the x and y values of the intersection point when writing the solution.
No. She used the wrong y-intercepts when graphing the equations.
No. She used the wrong slopes when graphing the equations.

Answer 1

To determine if Roxanne's solution of the intersection point (–3, –3) is correct, let's examine the equations she graphed:

1. **First equation**:
\( y = \frac{2}{3} x - 5 \)
To find the y-value when \( x = -3 \):
\[
y = \frac{2}{3}(-3) - 5 = -2 - 5 = -7
\]
So the point (-3, -7) is on the first line.

2. **Second equation**:
\( y = -2x + 3 \)
To find the y-value when \( x = -3 \):
\[
y = -2(-3) + 3 = 6 + 3 = 9
\]
So the point (-3, 9) is on the second line.

Since both equations yield different y-values when \( x = -3 \), we can conclude that the point (-3, -3) is not an intersection point of the lines defined by the given equations.

Therefore, the correct answer is:

**No. She switched the x and y values of the intersection point when writing the solution.**

The actual intersection point is likely different, but based on her calculations, (–3, –3) is incorrect because she did not correctly plot the lines according to the equations given.