Chapter 8.8, Problem 21E

To determine

To solve:

The given linear system of equations by graphing.

Answer to Problem 21E

The solution for given system of equations would be $(0,5)$ .

Explanation of Solution

Given:

A system of equations:

  $\begin{array}{l}4x+y=5\\ 3x+5y=25\end{array}$

Calculation:

First of all, we will convert our given equations in slope-intercept form as:

  $\begin{array}{l}4x+y=5\left(\text{Given equation}\right)\\ 4x-4x+y=5-4x\left(\text{Subtracting 4}x\text{ from both sides}\right)\\ y=-4x+5\end{array}$

  $\begin{array}{l}3x+5y=25\left(\text{Given equation}\right)\\ 3x-3x+5y=25-3x\left(\text{Subtracting 3}x\text{ from both sides}\right)\\ 5y=-3x+25\\ \frac{5y}{5}=\frac{-3x}{5}+\frac{25}{5}\left(\text{Dividing both sides by }5\right)\\ y=-\frac{3}{5}x+5\end{array}$

Upon graphing both equations, we will get our required graph as shown below:

  

Upon looking at our graph, we can see that both lines intersect at point $(0,5)$ . Therefore, the solution for given system of equations would be $(0,5)$ .