Question

find the ordered pair solutions for the system of equations.
\\(\

$$\begin{cases}y = x^{2}-5x - 4\\y=-2x\\end{cases}$$

\\)
(?, ) and ( , )
enter the smallest x first.

Explanation:

Step1: Set the two equations equal

Since $y = x^{2}-5x - 4$ and $y=-2x$, we set $x^{2}-5x - 4=-2x$.
$x^{2}-5x - 4+2x = 0$, which simplifies to $x^{2}-3x - 4 = 0$.

Step2: Factor the quadratic equation

Factor $x^{2}-3x - 4$: $x^{2}-3x - 4=(x - 4)(x+1)=0$.

Step3: Solve for x

Set each factor equal to zero:
If $x - 4=0$, then $x = 4$; if $x + 1=0$, then $x=-1$.

Step4: Find the corresponding y - values

When $x=-1$, $y=-2x=-2\times(-1)=2$.
When $x = 4$, $y=-2x=-2\times4=-8$.

Answer:

$(-1,2)$ and $(4,-8)$