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

$\left\{\begin{array}{l}y\le -\frac{3}{4}x+1\\ x\ge -5\end{array}\right.$

The system of inequality is$\left\{\begin{array}{l}y\le -\frac{3}{4}x+1\\ x\ge -5\end{array}\right.$

To find the solution of inequality by graphing

Graph the equation $y=-\frac{3}{4}x+1$with

slope $m=-\frac{3}{4}$and the $y-$intercept $1$.

It is a solid line since it contains the inequality $\le$.

Test the point$(0,0)$

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

Graph the line$x\ge -5$

It is a solid line since it contains the inequality $\ge$.

It is a vertical line.

Test the point$(0,0)$

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

The point where the boundary line intersect is a solution since it is a solution to both the inequalities.

The solution is all the points in the area shaded twice which appears as the darkest shaded region.

Choose $(0,0)$as a test point

Test for first inequality:

$0\le -\frac{3}{4}\left(0\right)+1$

$0\le 1$is true.

Test for second inequality:

$x\ge -5$

$0\ge -5$is true.

The region containing $(0,0)$is the solution to the system.