Question

Solve the system y = -x + 7 and y = 0.5(x - 3)2

Answer 1

y = 0.5(x - 3)2 -> y = x - 3

Answer 2

Can you confirm that 2y = 4

Answer 3

x=26/3, y=-5/3

Answer 4

\[\{x=5,y=2\} \]

Answer 5

y = -x + 7 and y = 0.5(x - 3)2
-x + 7 = (1/2)x^2 -1/2(6x) +1/2(9)
multiply everything by the lcd 2 the rearrange
x^2 - 4 x -5 = 0
(x - 5)(x + 1) = 0
x = 5, x = -1
y = -x + 7 when x = 5: -5 + 7 = 2
when x = -1 y = -(-1) + 7 = 8

(5, 2) and (-1, 8)

check in y = 0.5(x - 3)2
left =2
right 0.5(5-3)^2 = 0.5(2)^2= 2
left = right therefore (5,2) correct

left 8
right 0.5(-1 - 3)^2 = 0.5(-4)^2 = 0.5(16) = 8
left = right therefore (-1, 8) correct