Question

Which represents the solution(s) of the system of equations, y = x2 – 6x + 8 and y = –x + 4? Determine the solution set by graphing.

(1, 3) only
(2, 0) and (4, 0)
(1, 3) and (4, 0)
no solutions

Answer 1

they were right C was correct I finished the test so i can confirm

Explanation:

Answer 2

C) (1,3) and ( 4,0)

The intersecting points of two given curves are A( 1,3) and B(4,0)

Explanation:

Step(i):-

Given Parabola y = x² – 6x + 8 and straight line y = -x +4

y = x² – 6x + 8 ...(i)

y = -x +4 ...(ii)

Equating (i) and (ii) equations , we get

x² – 6x + 8 = -x +4

⇒ x² – 6x + 8 +x - 4 = 0

⇒ x² – 5x + 4 = 0

⇒ x² – 4x -x + 4 = 0

⇒ x ( x-4) -1( x -4) =0

⇒ (x -1) ( x -4) =0

⇒ x =1 and x = 4

Step(ii):-

Put x = 1 in equation y = -x +4

y = -1 +4 = 3

The first point A( 1,3)

Put x = 4 in equation y = -x +4

y = -4+4 =0

The second point B(4,0)

Final answer:-

The intersecting points of two given curves are A( 1,3) and B(4,0)