Question

Solve the system of equations graphicallySolution=?

Answer 1

The given system is

`\begin{cases}y=(5)/(2)x-8 \\ y=-(1)/(2)x-2\end{cases}`

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

`(5)/(2)x-8=-(1)/(2)x-2`

Let's solve for x

`\begin{gathered} (5)/(2)x+(1)/(2)x=8-2 \\ (6)/(2)x=6 \\ 3x=6 \\ x=(6)/(3) \\ x=2 \end{gathered}`

Then, we find y

`y=-(1)/(2)x-2=-(1)/(2)\cdot2-2=-1-2=-3`

The solution is (2, -3).

The image below shows the solution graphically.