Question

What are the solutions to the system of equations?

x = x^2 - 4x +3
y = -x +3

( , ) and ( , )

Answer 1

(0,3) and (3,0)

Explanation:

The first thing to do is graph the two equations to see where they intersect. Then you know what answer to look for. The graph is below. It was done on desmos.

I take it the first equation is a typo and should be y = x^2 - 4x + 3

Equate the two equations.

-x + 3 = x^2 -4x + 3 Subtract 3 from both sides

-x = x^2 - 4x + 3-3

-x = x^2 - 4x Add x to both sides.

0 = x^2 - 4x + x

0 = x^2 - 3x Factor

0 = x(x - 3)

So x can equal 0

or x can equal 3

In either case the right side will reduce to 0.

Case 1. x = 0

y= - x + 3

y = 0 + 3

y = 3

So the point is (0,3)

Case 2. x = 3

y = - x + 3

y = - 3 + 3

y = 0

So the point is (3,0)