Question

A student 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, 0)???????????? (3, 0).
Is the student correct? If not, explain why and find the
correct solutions.

Answer 1

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!