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

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

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

Step-by-step 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 -

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

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)