Question

solve the following system of equations algebraically:
y = x² + 5x - 17
y = x - 5
1 (-2, -7) and (-6, -11)
2 (2, -3) and (-6, -11)
3 (2, -3)
4 (2, -3) and (6, 1)

Explanation:

Step1: Set equations equal

$x^2 +5x -17 = x-5$

Step2: Simplify to quadratic

$x^2 +4x -12 =0$

Step3: Factor quadratic

$(x+6)(x-2)=0$

Step4: Solve for x

$x=-6, \, x=2$

Step5: Find matching y values

For $x=-6$: $y=-6-5=-11$; For $x=2$: $y=2-5=-3$

Answer:

1. $(2, -3)$ and $(-6, -11)$