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)

Answer 1

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**