Question

Solve a System of Linear Inequalities by Graphing
In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}x+3y<5\\ y\ge -\frac{1}{3}x+6\end{array}\right.$

Short answer

There is no solution of the system of the inequality $\left\{\begin{array}{l}x+3y<5\\ y\ge -\frac{1}{3}x+6\end{array}\right.$since it has no overlapped region.

Step-by-step solution

Step 1. Given

The system of inequality is$\left\{\begin{array}{l}x+3y<5\\ y\ge -\frac{1}{3}x+6\end{array}\right.$

To find the solution of inequality by graphing

Step 2. Graph the first inequality

Graph the line $x+3y=5$

It is a dashed line since it contains the inequality $<$.

And test the point $(0,0)$.

It is a solution to the given inequality, so shade the region that contains the point$(0,0)$

Step 3. Graph the second inequality

Graph the line $y=-\frac{1}{3}x+6$with slope

$m=-\frac{1}{3}$and $y-$intercept $6$

The boundary line is solid line since it contains the inequality$\ge$

Test the inequality with point$(0,0)$

It is not a solution so shade the region that does not contain the point $(0,0)$

Step 4. Solution of the inequality

From the graph, there is no overlapping region.

So the system of inequality does not contain solution.