which represents the solution(s) of the system of equations, $y = x^{2}-6x + 8$ and $y=-x + 4$? determine…

which represents the solution(s) of the system of equations, $y = x^{2}-6x + 8$ and $y=-x + 4$? determine the solution set by graphing.\n(1, 3) only\n(2, 0) and (4, 0)\n(1, 3) and (4, 0)\nno solutions

which represents the solution(s) of the system of equations, $y = x^{2}-6x + 8$ and $y=-x + 4$? determine the solution set by graphing.\n(1, 3) only\n(2, 0) and (4, 0)\n(1, 3) and (4, 0)\nno solutions

Answer

Explanation:

Step1: Set the two equations equal

Since (y = x^{2}-6x + 8) and (y=-x + 4), we set (x^{2}-6x + 8=-x + 4). [x^{2}-6x + 8+x - 4=0] [x^{2}-5x + 4=0]

Step2: Factor the quadratic equation

Factor (x^{2}-5x + 4) into ((x - 1)(x - 4)=0).

Step3: Solve for x

Using the zero - product property, if ((x - 1)(x - 4)=0), then (x-1 = 0) or (x - 4=0). So (x=1) or (x = 4).

Step4: Find the corresponding y - values

When (x = 1), (y=-1 + 4=3). When (x = 4), (y=-4 + 4=0).

Answer:

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