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)

y = 2x - 4....so sub in 2x - 4 for x in the other equation

y = x^2 - 6x + 12
2x - 4 = x^2 - 6x + 12
x^2 - 6x - 2x + 12 + 4 = 0
x^2 - 8x + 16 = 0
(x - 4)(x - 4) = 0

x - 4 = 0
x = 4

x - 4 = 0
x = 4

solution is (4,4)

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astha8579 astha8579 · Answer 2 · 2022-02-01T03:51:35-05:00

You can use any of the methods like substitution, graphing etc to solve the given system of equations.

The solution(s) of the given system of equations is given by

(x,y) = (4,4)

What are the solution(s) to a system of equations?

Solution to a system of equations are those values to variables which satisfy all the equations in that system simultaneously.

How to find the solutions to given system of equations?

We can try substitution here in which we can take value of y from first expression and substitute it in the second equation.

Thus,

\(y = x^2 - 6x + 12\\y = 2x - 4\\\\x^2 - 6x + 12 = 2x - 4\\x^2 -8x + 16 = 0\\x^2 - 4x - 4x + 16\\x(x-4) -4(x - 4) = 0\\(x-4)(x-4) = 0\\x = 4\)

Thus, x = 4. Putting this value in any of the equation we have for y, we get:

\(y = 2x - 4\\y = 2 \times 4 - 4 = 8 - 4\\ y = 4\)

Thus, the solution to the given system of equations is given by

(x,y) = (4,4)

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