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

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To determine whether Roxanne's solution (−3, −3) is correct for the equations \( y = 23x - 5 \) and \( y = -2x + 3 \), we should first find the intersection point by setting the two equations equal to each other.

  1. Set the equations equal: \[ 23x - 5 = -2x + 3 \]

  2. Solve for \( x \): \[ 23x + 2x = 3 + 5 \] \[ 25x = 8 \] \[ x = \frac{8}{25} \]

  3. Now substitute \( x = \frac{8}{25} \) into one of the original equations to find \( y \). We'll use \( y = -2x + 3 \): \[ y = -2\left(\frac{8}{25}\right) + 3 \] \[ y = -\frac{16}{25} + 3 \] \[ y = -\frac{16}{25} + \frac{75}{25} \] \[ y = \frac{59}{25} \]

So the intersection point, i.e., the solution to the system of equations, is \(\left(\frac{8}{25}, \frac{59}{25}\right)\) or approximately (0.32, 2.36).

Since Roxanne's solution of (−3, −3) is incorrect, the correct explanation is: No, she switched the x and y values of the intersection point when writing the solution.