Question

Find the solution(s) to the system of equations below using the graph only. y = x^2 y = -2x + 3 Support your answer algebraically. Show all work!

Answer 1

`(1,1)\text{ and }(-3,9)`

Explanation:

Graphically the solution are points of intersection between both graphs, just like this:

We have the following system of equations:

`\begin{gathered} y=x^2 \\ y=-2x+3 \end{gathered}`

We solve by means of equalization

`\begin{gathered} x^2=-2x+3 \\ x+2x-3=0 \\ (x-1)(x+3)=0 \\ x-1=0\rightarrow x=1 \\ x+3=0\rightarrow x=-3 \end{gathered}`

Now, for y:

`\begin{gathered} y=1^2=1 \\ y=(-3)^2=9 \end{gathered}`

Therefore, the solutions are:

`(1,1)\text{ and }(-3,9)`