Question

Roxanne graphed the system of equations to find the solution.

y=23x−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 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.

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.

Yes, she is correct.

Answer 1

To determine if Roxanne's solution of (−3, −3) is correct for the system of equations given, we can substitute x = -3 into both equations and see if it yields y = -3.

1. For the first equation \( y = 23x - 5 \):
\[
y = 23(-3) - 5 = -69 - 5 = -74
\]
This does not equal -3.

2. For the second equation \( y = -2x + 3 \):
\[
y = -2(-3) + 3 = 6 + 3 = 9
\]
This also does not equal -3.

Since neither equation gives us y = -3 when x = -3, Roxanne's solution is not correct.

The correct explanation is:
**No, she switched the x and y values of the intersection point when writing the solution.**