Chapter 9.7, Problem 4OE

To determine

To calculate: To find the number of real solutions of system of equations

Answer to Problem 4OE

Number of real solutions is $2$

Explanation of Solution

Given information: System of equations $y=x^2;y=2x$

Calculation:

Given the system of equations as follows:

  $\begin{array}{l}y=x^2----(1)\\ y=2x----(2)\end{array}$

Equation equations (1) and (2):

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

When $x=0$

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

When $x=2$

  $\begin{array}{l}y=2\left(2\right)\\ y=4\end{array}$

Thus, solutions are $\left(0,0\right)$ and $\left(2,4\right)$

Conclusion:

Hence, number of real solutions is $2$