Astudent worked out the following problem to find the solution of the system: y=x^2+3x-5 y=4x+1 here is the work the student did: y=x^2+3x-5 y=4x+1 x^2+3x-5=4x+1 x^2-x-6=0 (x-3)(x+2)=0 x=3 and x=-2 the equations intersect at (−2, (3, 0). is the student correct? if not, explain why and find the correct solutions.

The working is correct, BUT, they did not substitute their x values in which they have found into one of the equations to determine the y values. By using x = 3 and x = -2, sub them into equation 2 (mainly since it is simpler),

x = 3,                                  x = -2
y = 4x + 1                           y = 4x + 1
   = 4(3) + 1                           = 4(-2) + 1
   = 13                                    = -7

Therefore, the correct points of intersection are (3 , 13) and (-2 , -7)

Hope this helped!