Question

select the correct answer. solve the system of equations. $y = x + 3$ $y = x^2 - 2x - 1$ a. $(-1,2)$ and $(4,7)$ b. $(-1,7)$ and $(4,2)$ c. $(-1,4)$ and $(4,-1)$ d. $(1,4)$ and $(-4,-1)$

Explanation:

Step1: Set equations equal

$x + 3 = x^2 - 2x - 1$

Step2: Rearrange to quadratic form

$x^2 - 3x - 4 = 0$

Step3: Factor the quadratic

$(x - 4)(x + 1) = 0$

Step4: Solve for x-values

$x - 4 = 0 \implies x = 4$; $x + 1 = 0 \implies x = -1$

Step5: Find y for x=4

$y = 4 + 3 = 7$

Step6: Find y for x=-1

$y = -1 + 3 = 2$

Answer:

A. (-1,2) and (4,7)