Chapter 7.2, Problem 54E

To determine

To graph : the line in the system and check whether the system is consistent or inconsistent.

Explanation of Solution

Given information :

  $\{\begin{array}{l}5x-y=-4\\ 2x+\frac{3}{5}y=\frac{2}{5}\end{array}$

Graph: Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression ${\text{Y}}_1\text{=}5x-y=-4$ and ${\text{Y}}_2=2x+\frac{3}{5}y=\frac{2}{5}$ which is required to graph.

Step 4: Press GRAPH button to graph the function.

The graph is obtained as:

  

The system is consistent because the line of the given equation intersect each other and the point of intersection of both line is $x=-1.9$ and $y=-5.5$ .

Interpretation : From the above graph, it can be observed thatthe system is consistent because the line of given equation intersect each other and the solution of the system is $x=-1.9$ and $y=-5.5$ .