Question

find the ordered pair solutions for the system of equations.
$\begin{cases}y = x^{2}-3x - 10\\y=-x - 2end{cases}$
$(?, )$ and $( , )$
enter the smallest x first.

Explanation:

Step1: Set the equations equal

Since both expressions equal $y$, we set $x^{2}-3x - 10=-x - 2$.

Step2: Rearrange to standard - form

Move all terms to one side: $x^{2}-3x + x-10 + 2=0$, which simplifies to $x^{2}-2x - 8=0$.

Step3: Factor the quadratic equation

Factor $x^{2}-2x - 8$ as $(x - 4)(x+2)=0$.

Step4: Solve for x

Set each factor equal to zero: $x - 4=0$ gives $x = 4$; $x+2=0$ gives $x=-2$.

Step5: Find corresponding y - values

When $x=-2$, substitute into $y=-x - 2$, so $y=-(-2)-2=0$.
When $x = 4$, substitute into $y=-x - 2$, so $y=-4 - 2=-6$.

Answer:

$(-2,0)$ and $(4,-6)$