Question

Roxanne graphed the system of equations to find the solution.

y=2/3x−5
and y=−2x+3




She determined that the solution is (−3, −3)
. Is she correct? If not, choose the correct explanation

(1 point)
Responses

No, she used the wrong slopes when graphing the equations.
No, she used the wrong slopes when graphing the equations.

No, she used the wrong y-intercepts when graphing the equations.
No, she used the wrong y-intercepts when graphing the equations.

No, she switched the x and y values of the intersection point when writing the solution.
No, she switched the x and y values of the intersection point when writing the solution.

Yes, she is correct.
Yes, she is correct.

Answer 1

To verify if Roxanne's solution of (−3, −3) is correct, we need to check if this point satisfies both equations in the system:

1. \( y = \frac{2}{3}x - 5 \)
2. \( y = -2x + 3 \)

Let's substitute \( x = -3 \) and \( y = -3 \) into both equations.

**For the first equation:**
\[
y = \frac{2}{3}(-3) - 5 \\
-3 = -2 - 5 \\
-3 = -7 \quad \text{(This is not true)}
\]

**For the second equation:**
\[
y = -2(-3) + 3 \\
-3 = 6 + 3 \\
-3 = 9 \quad \text{(This is also not true)}
\]

Since (−3, −3) does not satisfy either equation, Roxanne is incorrect.

The appropriate response is:
**No, she used the wrong slopes when graphing the equations.**