Question

Solve the system of equations graphicallySolution=?

Answer 1

The given system is

$\begin{cases}y=\frac{5}{2}x-8 \\ y=-\frac{1}{2}x-2\end{cases}$

Given that y = y, let's combine the equations

$\frac{5}{2}x-8=-\frac{1}{2}x-2$

Let's solve for x

$\begin{gathered} \frac{5}{2}x+\frac{1}{2}x=8-2 \\ \frac{6}{2}x=6 \\ 3x=6 \\ x=\frac{6}{3} \\ x=2 \end{gathered}$

Then, we find y

$y=-\frac{1}{2}x-2=-\frac{1}{2}\cdot2-2=-1-2=-3$

The solution is (2, -3).

The image below shows the solution graphically.