For each ordered pair (x, y), determine whether it is a solution to the inequality 6x + 5y

Question

For each ordered pair (x, y), determine whether it is a solution to the inequality 6x + 5y < 2.

(7, -8)
(-4, -3)
(2, 0)
(-8, 6)

GPT-4o mini · Answer

To determine if each ordered pair $(x, y)$ is a solution to the inequality $6x + 5y < 2$, we will substitute the values of $x$ and $y$ into the inequality and check if the resulting statement is true. 1. For $(7, -8)$: $$ 6(7) + 5(-8) = 42 - 40 = 2 $$ We need to check if $2 < 2$. This is **false**. 2. For $(-4, -3)$: $$ 6(-4) + 5(-3) = -24 - 15 = -39 $$ We check if $-39 < 2$. This is **true**. 3. For $(2, 0)$: $$ 6(2) + 5(0) = 12 + 0 = 12 $$ We check if $12 < 2$. This is **false**. 4. For $(-8, 6)$: $$ 6(-8) + 5(6) = -48 + 30 = -18 $$ We check if $-18 < 2$. This is **true**. **Summary of results:** - $(7, -8)$: **Not a solution** - $(-4, -3)$: **A solution** - $(2, 0)$: **Not a solution** - $(-8, 6)$: **A solution**