# How do you tell whether the ordered pair (1,3) is a solution to y<=x+2, y>4x-1?

Dec 18, 2016

Because it does not hold for one of the inequalities this ordered pair is not a solution to the set of inequalities.

#### Explanation:

To make this determination you must substitute $1$ for $x$ in each inequality and $3$ for $y$ in each inequality and to see whether or not the inequalities hold:

Inequality 1)

$3 \le 1 + 2$

$3 \le 3$ This is true therefore the inequality holds.

Inequality 2)

$3 > \left(4 \times 1\right) - 1$

$3 > 4 - 1$

$3 > 3$ This is not true therefor the inequality does not hold.

Because it does not hold for one of the inequalities this ordered pair is not a solution to the set of inequalities.