Question

What are the solutions to the following system of equations? y=x^2-2x+48x+y=20

Answer 1

`\begin{gathered} y=x^2-2x+4 \\ y=20-8x \end{gathered}`

therefore we get

`\begin{gathered} 20-8x=x^2-2x+4\rightarrow \\ x^2+6x-16=0 \\ (x+8)(x-2)=0\rightarrow x=2\lor x=-8 \end{gathered}`

so the solutions of this system are

`\begin{gathered} (x,y)=(2,4) \\ (x,y)=(-8,84) \end{gathered}`