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 used the wrong slopes when graphing the equations. No, she used the wrong slopes 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. 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 verify whether Roxanne's solution (−3, −3) is correct for the system of equations \( y = 23x - 5 \) and \( y = -2x + 3 \), we can substitute the x-value and y-value into both equations.

1. Substitute \( x = -3 \) into the first equation:
\[
y = 23(-3) - 5 = -69 - 5 = -74
\]
This gives a y-value of -74, not -3.

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

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

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