# Thread: needdd major help solving a system

1. ## needdd major help solving a system

how wouls u solve this

y=x+4
x^2+y^2=16

the questions says:

solving a liner-quadratic system involves finding the values which satasfy a liner equation and a quadratic equation simultaneously. The method of substituting the inear equation into the quadratic equation should be used. The quadratic equation could b a parabola or a circle or any of the conic sections. The values found in the solution represent the co-ordiantes of the point(s) of intersection of the two graphs.

solve the set of real numbers.

can you show me how to do this and explain the steps please

2. Hello, kishan!

$\begin{array}{cc}y\:=\:x+4 \\ x^2+y^2\:=\:16\end{array}$

"The method of substituting the inear equation into the quadratic equation should be used."
What part of that don't you understand?

Substitute $y\:=\:x+4$ into $x^2 + y^2\:=\:16$

We have: . $x^2 + (x + 4)^2\:=\:16$

Then: . $x^2 + x^2 + 8x + 16 \:=\:16\quad\Rightarrow\quad 2x^2 + 8x\:=\:0$

Factor: . $2x(x+4)\:=\:0$

And we have two roots: . $\begin{array}{cc}2x\:=\:0 \\ x + 4\:=\:0 \end{array}
\begin{array}{cc}\Rightarrow \\ \Rightarrow \end{array}
\begin{array}{cc}x\,=\,0 \\ x\,=\,\text{-}4\end{array}$

The corrsponding y-values are: . $y \:=\:4,\,0$

Answers: . $\begin{Bmatrix}x=0, & y=4 \\ x=\text{-}4, & y=0\end{Bmatrix}$