Question

Is each ordered pair a solution of the inequality? $$2 x+2 y \leq 0 ;(-1,-1),(1,1)$$

Short answer

The ordered pair \(-1, -1\) is a solution to the inequality, while the ordered pair \(1, 1\) is not.

Step-by-step solution

Substitute Ordered Pair 1

Start by substituting the first ordered pair, \(-1,-1\), into the inequality \(2x + 2y \leq 0\). The inequality becomes \(2(-1) + 2(-1) \leq 0\), which simplifies to \(-4 \leq 0\).

Check Validity of Pair 1

The inequality \(-4 \leq 0\) is true, so \(-1, -1\) is a solution to the inequality.

Substitute Ordered Pair 2

Next, substitute the second ordered pair, \(1,1\), into the inequality. The inequality becomes \(2(1) + 2(1) \leq 0\), which simplifies to \(4 \leq 0\).

Check Validity of Pair 2

The inequality \(4 \leq 0\) is false, so \(1, 1\) is not a solution to the inequality.