91Ó°ÊÓ

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

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 $≤$.

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$xâ‰\yen -5$

It is a solid line since it contains the inequality $â‰\yen$.

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:

$0≤-\frac{3}{4}\left(0\right)+1$

$0≤1$is true.

Test for second inequality:

$xâ‰\yen -5$

$0â‰\yen -5$is true.

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