Chapter 9.8, Problem 20PPE

To determine

To solve given equations using substitution.

Answer to Problem 20PPE

  $\begin{array}{l}x=-7,-10\\ y=100,130\end{array}$

Explanation of Solution

Given information :

Given equations,

  $\begin{array}{l}y=x^2+7x+100\\ y+10x=30\end{array}$

In the given equations, we shall substitute the value of one variable in the other equation to solve.

Given equations are,

  $\begin{array}{l}y=x^2+7x+100\\ y+10x=30\text{ or }y=30-10x\end{array}$

Substitute the value of $y$ in equations we get,

  $\begin{array}{l}{x}^2+7x+100=30-10x\\ x^2+17x+70=0\end{array}$

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,

  $\begin{array}{l}x=\frac{-17\pm \sqrt{{\left(17\right)}^2-4\left(70\right)}}{2\left(1\right)}\\ x=\frac{-17\pm \sqrt{9}}{2}\\ x=-7,-10\end{array}$

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

We get $y=100,130$