Question

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.

Which represents the solution(s) of this system of equations?


(4, 4)

(–4, –12)

(4, 4) and (–4, 12)

(–4, 4) and (4, 12)

Answer 1

(4,4)

Explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).