Chapter 9, Problem 61SGR

To determine

To solve: the given system of equations.

Answer to Problem 61SGR

The system of equation does not have any real solution.

Explanation of Solution

Given information:

A system of equation is given as

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

Calculation:

Consider the given system of equation.

  $\begin{array}{l}y=x^2+9\mathrm{......}(1)\\ y=x\mathrm{......}(2)\end{array}$

Now, substitute equation (2) in equation (1).

  $\begin{array}{c}x=x^2+9\\ x^2-x+9=0\\ x=\frac{1\pm \sqrt{1-4\cdot 9\cdot 1}}{2\cdot 1}\\ =\frac{1\pm \sqrt{-35}}{2}\end{array}$

Therefore, the system of equation does not have any real solution.

Graph:

Graph the equations to verify the result.

  

There is no point of intersection.