What are the solutions to the system of equations? y=2x^2−6x+3 (both of the y= are in the one bracket)
{
y=x−2
(1, −1) and (5, 3)
(3, 1) and (2.5, 0.5)
(2.5, 0.5) and (4, 2)
(1, −1) and (2.5, 0.5)
y = 2x^2 - 6x + 3
y = x - 2
Set the y's equal and solve for x
2x^2 - 6x + 3 = x - 2 subtract x , add 2 from/to each side
2x^2 - 7x + 5 = 0 factor, if possible
(2x -5) ( x - 1) = 0
Set each factor to 0 and solve for x
2x - 5 = 0 x - 1 =0
2x = 5 x = 1
x = 5/2 = 2.5 x = 1
So y = x - 2 = 2.5 - 2 = 0.5 or y = x - 2 = 1 - 2 = -1
So {x,y} = { 2.5, 0.5} or { 1, -1 }