Question

find the ordered pair solution for the system of equations.
$\begin{cases}y = x^{2}+4\\y = 4xend{cases}$
(?, )
enter the x value first.

Explanation:

Step1: Set the two equations equal

Since $y = x^{2}+4$ and $y = 4x$, we set $x^{2}+4=4x$.
$x^{2}-4x + 4=0$

Step2: Factor the quadratic equation

The quadratic equation $x^{2}-4x + 4$ is a perfect - square trinomial. It can be factored as $(x - 2)^{2}=0$.

Step3: Solve for x

Taking the square root of both sides of $(x - 2)^{2}=0$, we get $x-2 = 0$, so $x = 2$.

Step4: Solve for y

Substitute $x = 2$ into $y = 4x$. Then $y=4\times2=8$.

Answer:

$(2,8)$