91Ó°ÊÓ

The system of inequalities, $\left\{\begin{array}{l}x-5y>10\\ 2x+3y>-2\end{array}\right.$

$(x,y)=(3,-1)$

Substitute the point $(3,-1)$in the system of inequalities.

$x-5y>10$

$\left(3\right)-5(-1)>10$

$3+5>10$

$8>10$

Hence the equation does not hold true

Substitute the point $(3,-1)$ in the system of inequalities.

$2x+3y>-2$

$2\left(3\right)+3(-1)>-2$

$6-3>-2$

$3>-2$which is true.

The ordered pair $(3,-1)$made one inequality true, but the other one is false.

Therefore, $(3,-1)$ is not a solution to this system.

Substitute the point $(6,-3)$in the system of inequality

$x-5y>10$

$\left(6\right)-5(-3)>10$

$6+15>10$

$21>10$ holds true.

Substitute the point $(6,-3)$in the system of inequalities.

$2x+3y>-2$

$2\left(6\right)+3(-3)>-2$

$12+(-9)>-2$

$3>-2$holds true.

The ordered pair $(6,-3)$made both the inequality true.

Therefore, $(6,-3)$is a solution to this system.