Question

solve the following system of equations algebraically:
y = x² - x - 65
y = -x - 1
answer
attempt 1 out of 2
two solutions
and

Explanation:

Step1: Set equations equal to each other

Since both expressions equal $y$, set them equal:
$x^2 - x - 65 = -x - 1$

Step2: Simplify the equation

Cancel $-x$ on both sides, then rearrange:
$x^2 - 65 = -1$
$x^2 = 64$

Step3: Solve for $x$

Take square root of both sides:
$x = \pm\sqrt{64} = 8 \text{ or } -8$

Step4: Find $y$ for $x=8$

Substitute $x=8$ into $y=-x-1$:
$y = -8 - 1 = -9$

Step5: Find $y$ for $x=-8$

Substitute $x=-8$ into $y=-x-1$:
$y = -(-8) - 1 = 8 - 1 = 7$

Answer:

$(8, -9)$ and $(-8, 7)$