Solve the system y = -x + 7 and y = 0.5(x - 3)^2
show all work.

x=-1, y=8

or

x=5, y=2

Step-by-step explanation:

if you rewrite the first as x = 7-y (bring x to the left, y to the right) you can substitute it in the second:

y = 0.5(7-y-3)²

then work out the quadratic factor:

y = 0.5(4² -8y + y²)

2y = y² - 8y + 16

y² - 10y + 16 = 0

(y-8)(y-2) = 0

y=8 or y=2

using x = 7-y you can match the x with that:

y=8 => x = 7-8 = -1

y=2 => x = 7-2 = 5

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)