Question

Solve the system of equations.y=x+2y=x² +7x+10INOA (-2-4) and (4-6)OB (2.4) and (4.6)OC(-20) and (-4-2)OD. (-2-2) and (-4.0)

Answer 1

We will have the following:

$\begin{gathered} y=x+2 \\ \\ and \\ \\ y=x^2+7x+10 \end{gathered}$

So:

$\begin{gathered} x^2+7x+10=x+2\Rightarrow x^2+6x+8=0 \\ \\ \Rightarrow x=\frac{-6\pm\sqrt{(6)^2-4(1)(8)}}{2(1)} \\ \\ \Rightarrow x=-4 \\ \\ And \\ \\ \Rightarrow x=-2 \end{gathered}$

Now, we determine the y-components, that is:

$\begin{gathered} y_1=-4+2\Rightarrow y_1=-2 \\ \\ And \\ \\ y_2=-2+2\Rightarrow y_2=9 \end{gathered}$

So, the points are:

$\begin{gathered} (-4,-2) \\ \\ and \\ \\ (-2,0) \end{gathered}$