Chapter 9.8, Problem 15PPE

To determine

To solve given equations using elimination.

Answer to Problem 15PPE

  $\begin{array}{l}x=2,-1\\ y=4,1\end{array}$

Explanation of Solution

Given information :

Given equations,

  $\begin{array}{l}y=x^2\\ y=x+2\end{array}$

In the given equations, we shall subtract one equation from other in order to eliminate one variable.

Given equations are,

  $\begin{array}{l}y=x^2\\ y=x+2\end{array}$

Subtract both equations we get,

  $\begin{array}{l}y-y=\left(x^2\right)-\left(x+2\right)\\ 0=x^2-x-2\end{array}$

Now we know that the solution of a standard quadratic equation $a{x}^2+bx+c=0$ is given by $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Hence the solution of the given equation is,

  $\begin{array}{l}x=\frac{1\pm \sqrt{{\left(-1\right)}^2-4\left(-2\right)}}{2\left(1\right)}\\ x=\frac{1\pm \sqrt{9}}{2}\\ x=2,-1\end{array}$

Now put both values of $x$ in any give equation to determine the values of $y$ ,

We get $y=4,1$