Chapter 7.1, Problem 57E

To determine

Tofind:The intersection point of the system of equations $\{\begin{array}{c}y=\sqrt{x}+4\\ y=2x+1\end{array}$ using graphical utility and verify the result by checking them in the original system.

Answer to Problem 57E

The intersection point of the system of equations $\{\begin{array}{c}y=\sqrt{x}+4\\ y=2x+1\end{array}$ is $\left(2.25,5.5\right)$ .

Explanation of Solution

Given information:

The given system of equations is $\{\begin{array}{c}y=\sqrt{x}+4\\ y=2x+1\end{array}$ .

Calculation:

Draw the graph for the equations $y=\sqrt{x}+4$ and $y=2x+1$ .

  

From the above graph, the intersection point is $\left(2.25,5.5\right)$ . So, the solution of the system of equations $\{\begin{array}{c}y=\sqrt{x}+4\\ y=2x+1\end{array}$ is $\left(2.25,5.5\right)$ .

Verify the solution by substituting the values of intersection point in the system of equations.

Substitute $2.25$ for $x$ and $5.5$ for $y$ in the first equation.

  $\begin{array}{c}y=\sqrt{x}+4\\ 5.5=\sqrt{2.25}+4\\ 5.5=5.5\end{array}$

Substitute $2.25$ for $x$ and $5.5$ for $y$ in the second equation.

  $\begin{array}{c}y=2x+1\\ 5.5=2\left(2.25\right)+1\\ 5.5=\left(4.5\right)+1\\ 5.5=5.5\end{array}$

From the above, it is clear that both the equations are satisfied. So, the ordered pair $\left(2.25,5.5\right)$ is a solution of the system of equations.

Therefore, the intersection point of the system of equations $\{\begin{array}{c}y=\sqrt{x}+4\\ y=2x+1\end{array}$ is $\left(2.25,5.5\right)$ .