Question

Help? >K12<
On a math test, Amy was asked to find the point(s) where the equations y = x2 + 3x – 5 & y = 4x + 1 intersect. Amy’s solution is shown below.
Amy’s solution: y = x2 + 3x – 5 y = 4x + 1 x2 + 3x – 5 = 4x + 1 x2 – x – 6 = 0 (x – 3) (x + 2) = 0 x = 3 or x = -2 The graphs intersect at (-2, 0) and (3, 0)
a) Is Amy’s solution correct? Explain why or why not.
b) If Amy’s solution is incorrect, show the correct work for this problem. Answer:

Answer 1

The correct answer is a) Amy's solutions are correct.

Since she wanted the intersection point of the equations, she had to set them equal.  Once she did she had

x²+3x-5=4x+1

Gathering the variables on one side of the equation, she subtracted 4x from each side:
x²+3x-5-4x=4x+1-4x
x²-x-5=1

Quadratics should be equal to 0 when we solve them, so she subtracted 1 from each side:
x²-x-5-1=1-1
x²-x-6=0

She then factored her expression; factors of -6 that sum to -1 are -3 and 2:
(x-3)(x+2)=0

Using the zero product property we know that either x-3=0 or x+2=0; therefore x=3 or x=-2.