Question

What are the solutions to the following system of equations? Select the correct answer below. y = x^2 − 4x + 3 2x + y = 6

Answer 1

2x+y=6

y=6-2x and y=x^2-4x+3

The solution occurs when they are equal so we can say y=y which is:

x^2-4x+3=6-2x  add 2x to both sides

x^2-2x+3=6  subtract 6 from both sides

x^2-2x-3=0  factor

(x+1)(x-3)=0

So x=-1 and 3, using y=6-2x we find the corresponding y values...

y(-1)=6--2=8, y(3)=6-6=0 so the two solutions are the points:

(-1,8) and (3,0)