Question

Check whether each ordered pair is a solution of the inequality. $$5 x+y>5 ;(5,5),(-5,-5)$$

Short answer

The ordered pair (5, 5) is a solution to the inequality, while the ordered pair (-5, -5) is not a solution to the inequality.

Step-by-step solution

Substitute the first ordered pair

Start with the first ordered pair which is (5,5). Substitute x = 5 and y = 5 into the inequality. You should write it as \(5(5) + 5 > 5\).

Evaluate the inequality with the first pair

Calculate the left side of the inequality by performing the multiplication and addition. It becomes \(25 + 5 > 5\) which simplifies to \(30 > 5\). Since 30 is indeed greater than 5, the first ordered pair (5,5) is a solution to the inequality.

Substitute the second ordered pair

Now proceed with the second ordered pair, which is (-5,-5). Substitute x = -5 and y = -5 into the inequality. You should write it as \(5(-5) -5 > 5 \).

Evaluate the inequality with the second pair

Calculate the left side of the inequality by performing the multiplication and addition. It becomes \(-25 - 5 > 5\) which simplifies to \(-30 > 5\). Since -30 is not greater than 5, the second ordered pair (-5,-5) is not a solution to the inequality.