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 Yes, she is correct. Yes, she is correct. 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. No, she used the wrong slopes when graphing the equations. No, she used the wrong slopes when graphing the equations.

Answer 1

To determine if Roxanne's solution of (−3, −3) is correct, we need to find the intersection point of the equations \(y = 23x - 5\) and \(y = -2x + 3\).

1. Set the equations equal to each other since they both equal \(y\): \[ 23x - 5 = -2x + 3 \]

2. Combine the terms: \[ 23x + 2x = 3 + 5 \] \[ 25x = 8 \]

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

4. Substitute \(x = \frac{8}{25}\) back into either equation to find \(y\). Let's use \(y = -2x + 3\): \[ y = -2 \left(\frac{8}{25}\right) + 3 = -\frac{16}{25} + 3 = -\frac{16}{25} + \frac{75}{25} = \frac{59}{25} \]

Thus, the intersection point is \(\left(\frac{8}{25}, \frac{59}{25}\right)\), which is not \((-3, -3)\).

Therefore, Roxanne is not correct and the correct explanation is:

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