the first two steps in determining the solution set of the system of equations, y = x² - 6x + 12 and y = 2x…

the first two steps in determining the solution set of the system of equations, y = x² - 6x + 12 and y = 2x - 4, algebraically are shown in the table.\n| step | equation |\n| ---- | ---- |\n| step 1 | x² - 6x + 12 = 2x - 4 |\n| step 2 | x² - 8x + 16 = 0 |\nwhich represents the solution(s) of this system of equations?\n(4, 4)\n(-4, -12)\n(4, 4) and (-4, 12)\n(-4, 4) and (4, 12)

the first two steps in determining the solution set of the system of equations, y = x² - 6x + 12 and y = 2x - 4, algebraically are shown in the table.\n| step | equation |\n| ---- | ---- |\n| step 1 | x² - 6x + 12 = 2x - 4 |\n| step 2 | x² - 8x + 16 = 0 |\nwhich represents the solution(s) of this system of equations?\n(4, 4)\n(-4, -12)\n(4, 4) and (-4, 12)\n(-4, 4) and (4, 12)

Answer

Explanation:

Step1: Factor the quadratic equation

Given $x^{2}-8x + 16=0$, which is a perfect - square trinomial and can be factored as $(x - 4)^{2}=0$.

Step2: Solve for x

Taking the square root of both sides of $(x - 4)^{2}=0$, we get $x-4 = 0$, so $x = 4$.

Step3: Solve for y

Substitute $x = 4$ into the linear equation $y=2x - 4$. Then $y=2\times4-4=4$.

Answer:

A. $(4,4)$