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.

We have that

y=x²+3x-5
y=4x+1

using a graph tool
see the attached figure

the solution are the points
(-2,-7)
(3,13)

the solution obtained by the student
(-2,0)
(3,0)
is incorrect because the values of the coordinate y are incorrect
the values of x are correct
x1=-2
x2=3

with those values of x obtained, the student had to substitute it in any of the two equations to obtain the value of y
so
for x=3
y=4x+1------> 4*(3)+1-----> y=13

for x=-2
y=4x+1------> 4*(-2)+1-----> y=-7

Where m is the slope of the line and b is the y-intercept of the line, or the y-coordinate of the point at which the line crosses the y-axis. to write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. this is the value of m in the equation.