Question

the first three steps in determining the solution set of the system of equations algebraically are shown,
y = x² - x - 3
y = -3x + 5

step	equation
2	0 = x² + 2x - 8
3	0 = (x - 2)(x + 4)

what are the solutions of this system of equations?
○ (-2, -1) and (4, 17)
○ (-2, 11) and (4, -7)
○ (2, -1) and (-4, 17)
○ (2, 11) and (-4, -7)

Explanation:

Step1: Solve for x from factored form

From \(0=(x - 2)(x + 4)\), we set each factor to zero:
\(x - 2 = 0\) gives \(x = 2\); \(x + 4 = 0\) gives \(x=-4\).

Step2: Find corresponding y using \(y=-3x + 5\)

For \(x = 2\): \(y=-3(2)+5=-6 + 5=-1\).
For \(x=-4\): \(y=-3(-4)+5 = 12 + 5 = 17\).

Answer:

(2, -1) and (-4, 17)