# How do you determine ordered pairs are part of the solution set of inequalities ex: 3x+y<=6 for (4,3),(-2,4),(-5,-3),(3,-3)?

Apr 3, 2015

Assuming I understand the question; you need to know which of the pairs $\left(4 , 3\right) , \left(- 2 , 4\right) , \left(- 5 , - 3\right) ,$ and $\left(3 , - 3\right)$
satisfy the inequality
$3 x + y \le 6$

For each pair
substitute their values for $x$ and $y$
in the expression $3 x + y$
and select only those that evaluate as $\le 6$

For (4,3)
$3 \left(4\right) + 3 = 15$
which is not $\le 6$ and is therefore not part of the solution set.

Continue with the other 3 possible pairs.