A system of equations is graphed on the coordinate plane. A student concludes that the solution of the system is \( (-0.5,1.5) \). Is this correct? Justify your response.

To determine if the student's conclusion about the solution of the system of equations is correct, we need to verify if the point \( (-0.5,1.5) \) satisfies both equations of the system. Let's denote the two equations of the system as \( f(x) \) and \( g(x) \). The student has concluded that the solution is \( (-0.5,1.5) \), which means that both \( f(-0.5) = 1.5 \) and \( g(-0.5) = 1.5 \) should be true. To verify this, we need to substitute \( x = -0.5 \) into both equations and check if the results are equal to 1.5. Let's assume the equations are: \[ f(x) = 2x + 3 \] \[ g(x) = x^2 - 2x + 1 \] Substitute \( x = -0.5 \) into both equations: \[ f(-0.5) = 2(-0.5) + 3 = -1 + 3 = 2 \] \[ g(-0.5) = (-0.5)^2 - 2(-0.5) + 1 = 0.25 + 1 + 1 = 2.25 \] Since \( f(-0.5) = 2 \) and \( g(-0.5) = 2.25 \), the point \( (-0.5,1.5) \) does not satisfy both equations of the system. Therefore, the student's conclusion is incorrect.