Question

solve the following system of equations.
$y = x^2 - 2x + 7$
$y = -8x - 2$
if there is no solution, click
o solution\.
if there is more than one solution, use the \or\ button.
$(x, y) = (\square, \square)$

Explanation:

Step1: Set equations equal

Since $y=y$, substitute the two expressions:
$x^2 - 2x + 7 = -8x - 2$

Step2: Rearrange to standard quadratic form

Bring all terms to left side:
$x^2 - 2x + 8x + 7 + 2 = 0$
$x^2 + 6x + 9 = 0$

Step3: Factor the quadratic

Factor the perfect square trinomial:
$(x + 3)^2 = 0$

Step4: Solve for $x$

Take square root of both sides:
$x + 3 = 0$
$x = -3$

Step5: Find $y$ using $x=-3$

Substitute $x=-3$ into $y=-8x-2$:
$y = -8(-3) - 2 = 24 - 2 = 22$

Answer:

$(x,y)=(-3, 22)$