Question

What is (are) the solution(s) to the system of equations y = -x + 4 and y = -x^2 + 4 ?

Answer 1

Given:

`\begin{gathered} y=-x+4----(1) \\ y=-x^2+4----(2) \end{gathered}`

Required:

To find the solutions to the given equations.

Step-by-step explanation:

Put equation 1 in 2, we get

`\begin{gathered} -x+4=-x^2+4 \\ \\ -x+4+x^2-4=0 \\ \\ x^2-x=0 \\ \\ x(x-1)=0 \\ \\ x=0,1 \end{gathered}`

When x=0,

`\begin{gathered} y=-0+4 \\ y=4 \end{gathered}`

When x=1,

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

Final Answer:

The solution are

`x=0,1`

The solution sets are

`\begin{gathered} (0,4)\text{ and} \\ (1,3) \end{gathered}`