Question

For each ordered pair (x, y), determine whether it is a solution to the inequality 8x+3y≤-3.
(x, y)
Is it a
solution?
Yes
No
(4, - 6)


(-2,0)


(-3,7)


(-2, - 5)

Answer 1

To determine whether each ordered pair \((x, y)\) is a solution to the inequality \(8x + 3y \leq -3\), we'll substitute the values of \(x\) and \(y\) into the inequality and check if it holds true.

1. **For (4, -6)**:
\[
8(4) + 3(-6) \leq -3
\]
\[
32 - 18 \leq -3
\]
\[
14 \leq -3 \quad \text{(False)}
\]
**Is it a solution? No**

2. **For (-2, 0)**:
\[
8(-2) + 3(0) \leq -3
\]
\[
-16 + 0 \leq -3
\]
\[
-16 \leq -3 \quad \text{(False)}
\]
**Is it a solution? No**

3. **For (-3, 7)**:
\[
8(-3) + 3(7) \leq -3
\]
\[
-24 + 21 \leq -3
\]
\[
-3 \leq -3 \quad \text{(True)}
\]
**Is it a solution? Yes**

4. **For (-2, -5)**:
\[
8(-2) + 3(-5) \leq -3
\]
\[
-16 - 15 \leq -3
\]
\[
-31 \leq -3 \quad \text{(False)}
\]
**Is it a solution? No**

In summary, the results are as follows:
- (4, -6): No
- (-2, 0): No
- (-3, 7): Yes
- (-2, -5): No