Question

Is (7, –4) a solution to this system of inequalities?

y≤ 1/7x− 5
y≤ –1/7x− 3

Answer 1

To determine if the point (7, –4) is a solution to the system of inequalities, we need to substitute \( x = 7 \) and \( y = -4 \) into each inequality and check if the inequalities hold true.

1. **First Inequality:**
\[
y \leq \frac{1}{7}x - 5
\]
Substitute \( x = 7 \):
\[
-4 \leq \frac{1}{7}(7) - 5
\]
This simplifies to:
\[
-4 \leq 1 - 5
\]
\[
-4 \leq -4
\]
This is true.

2. **Second Inequality:**
\[
y \leq -\frac{1}{7}x - 3
\]
Substitute \( x = 7 \):
\[
-4 \leq -\frac{1}{7}(7) - 3
\]
This simplifies to:
\[
-4 \leq -1 - 3
\]
\[
-4 \leq -4
\]
This is also true.

Since the point (7, -4) satisfies both inequalities, it is indeed a solution to the system of inequalities.