Chapter 9.8, Problem 5LC

To determine

To solve given equations using two different methods.

Explanation of Solution

Given information :

Given equations,

  $\begin{array}{l}y=2x^2+10x+9\\ y=x\end{array}$

1. Graphing method.

Here we shall plot the graph for the given equations,

We get,

  

Green line represents the equation $y=2x^2+10x+9$

Blueline represents the equation $y=x$

Hence the solutions are (-1.5, -1.5) (-3, -3)

2. Using eliminating method.

Given equations,

  $\begin{array}{l}y=2x^2+10x+9\\ y=x\end{array}$

Subtracting both equations we get,

  $\begin{array}{l}y-y=2x^2+10x+9-x\\ 0=2x^2+9x+9\end{array}$

Hence the value of $x$ is,

  $\begin{array}{l}x=\frac{-9\pm \sqrt{9^2-4\left(2\right)\left(9\right)}}{2\left(2\right)}\\ x=\frac{-9\pm \sqrt{9}}{4}\\ x=-3,-1.5\end{array}$

Put the values of $x$ in any given equations we get the solutions as,

(-3, -3) (-1.5, -1.5)

In the given equations substitution and elimination both are preferable method.