Chapter 2.1, Problem 14E

To determine

To find: of the system of given equations by graphing.

Answer to Problem 14E

  $\begin{array}{l}x=5\\ y=0\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}x=5\mathrm{...}\left(1\right)\\ 4x+5y=20\mathrm{...}\left(2\right)\end{array}$

Calculation:

According to equation (1), the points of coordinate will be $\left(5,0\right)$ because it is a vertical line.

Convert equation (2) into slope intercept form to evaluate the value of slope and y-intercept as follows:

  $\begin{array}{c}4x+5y=20\\ 5y=-4x+20\\ y=-\frac{4}{5}x+\frac{20}{5}\\ =-\frac{4}{5}x+4\end{array}$

Thus, the value of slope is $-\frac{4}{5}$ and y-intercept is 4.

Put different values of x in equation (2) to get different values of y, and then graph the line as follows:

  

So, the point of intersection is $\left(5,0\right)$ . That is, the value of x and y is 5 and 0 respectively.