Question

Solve the system of equations algebraically: y = -x2 + 2x + 4 and y = 4 - x.

Answer 1

`\begin{gathered} y=\text{ -x}^2\text{ +2x+4} \\ y=\text{ 4 -x} \\ \\ 4\text{ -}x=\text{ -}x^2+2x+4 \\ \text{ -}x=\text{ -1\lparen}x^2\text{ - }2x) \\ x=\text{ }x^2\text{ - }2x \\ 0=\text{ }x^2\text{ - }3x \\ 0=\text{ }x(x\text{ - 3\rparen} \\ So \\ x=0 \\ x=3 \end{gathered}`

So:

`\begin{gathered} y=\text{ 4 -0} \\ y=4 \\ \\ y=4\text{ - 3} \\ y=\text{ 1} \end{gathered}`

Then, the points are (3,1) and (0,4)