Chapter 6.1, Problem 7P

Solve each system by graphing. Check your solution.

$y=\frac{3}{4}x-5$

$3x-4y=20$

To determine

To find: The solution of the system of equations:

  $\begin{array}{l}y=\frac{3}{4}x-5\\ 3x-4y=20\end{array}$

Answer to Problem 7P

The graph of the system is

  

There is an infinite number of solutions for the given system of equations.

Explanation of Solution

Given information:

The system is

  $\begin{array}{l}y=\frac{3}{4}x-5\\ 3x-4y=20\Rightarrow y=\frac{3}{4}x-5\end{array}$

The equation $y=\frac{3}{4}x-5$ has the slope $\frac{3}{4}$ and y -intercept of $-5$ . So plot a point at $-5$ on the y -axis. Then go up 3 right 4 from the y -intercept to plot a second point. Now, draw a line passing through these two points as shown in the graph in red color.

However, the second equation is an alternative form of the second equation. So the lines of the given system coincide on one another as shown in the below:

  

Conclusion:

Observing the graph, there would be an infinite number of solutions for the system.