91Ó°ÊÓ

The system of inequalities $\left\{\begin{array}{l}y>\frac{1}{3}x+2\\ x-\frac{1}{4}y≤10\end{array}\right.$

To find if the ordered pair $(6,5)$is a solution to the given inequality.

Substitute $(6,5)$in the inequality,

$y>\frac{1}{3}x+2$

$5>\frac{1}{3}\left(6\right)+2$

$5>4$ is true.

Substitute $(6,5)$in the inequality $x-\frac{1}{4}y≤10$,

$6-\frac{1}{4}\left(5\right)≤10$

$\frac{24-5}{4}≤10$

$\frac{19}{4}≤10$

$19≤40$is true.

The ordered pair$(6,5)$ made both the inequality true.

So the ordered pair$(6,5)$ is a solution to the inequality.

The system of inequalities $\left\{\begin{array}{l}y>\frac{1}{3}x+2\\ x-\frac{1}{4}y≤10\end{array}\right.$

To find if the ordered pair $(15,8)$is a solution to the given inequality.

Substitute $(15,8)$in the inequality,

$y>\frac{1}{3}x+2$

$8>\frac{1}{3}\left(15\right)+2$

$8>5+2$

$8>7$ is true.

Substitute $(15,8)$in the inequality,

$x-\frac{1}{4}y≤10$

$15-\frac{1}{4}\left(8\right)≤10$

$15-2≤10$

$13≤10$is false.

So the ordered pair $(15,8)$made one of the inequality true and the other one false.

So the ordered pair $(15,8)$is not a solution to the system of inequalities.