Chapter 12.1, Problem 40STP

To determine

To find : Solution of given system of equations.

Answer to Problem 40STP

  $\left\{(\sqrt{17}-1),(\sqrt{17}+1),(\sqrt{17}-1,-\sqrt{17}+1)\right\}$

Explanation of Solution

Given information :

The given equation is,

  $x^2+y^2=36$.............(1)

  $y=x+2$.............(2)

Formula Used:

Method of substitution.

Calculation :

By equation (1) and (2), we get

  $\begin{array}{}$ x^2+{(x+2)}^2=36$$ 2x^2+4x+4-36=0$$ 2\left(x^2+2x-16\right)=0$$ x^2+2x-16=0$$ {(x+1)}^2=17$$ \Rightarrow x=\pm \sqrt{17}-1$\end{array}$

So, $x_1=\sqrt{17}-1,x_2=-\sqrt{17}-1$

  $y_1=+\sqrt{17}+1,y_2=-\sqrt{17}+1$