Chapter 9, Problem 21CT

To determine

To solve given equations.

Answer to Problem 21CT

The solutions are (4, 5) (-12, 85)

Explanation of Solution

Given information:

  $\begin{array}{l}y=x^2+3x-23\\ y=25-5x\end{array}$

Here we shall substitute the value of $y$ in the first equation in order to solve.

Hence we get,

  $\begin{array}{l}\left(25-5x\right)=x^2+3x-23\\ x^2+3x-23-25+5x=0\\ x^2+8x-48=0\end{array}$

Now we shall determine the values of $x.$

  $\begin{array}{l}x=\frac{-8\pm \sqrt{8^2-4\left(-48\right)}}{2}\\ x=\frac{-8\pm \sqrt{256}}{2}\\ x=4,-12\end{array}$

Now we shall put the values of $x$ in any given equation to determine the values of $y.$

We get $y=5,85$

Therefore the solutions are (4, 5) (-12, 85)