Question

Is (7, –8) a solution to this system of inequalities?

y < 3/7x+ 7
y ≥ –x + 10

Answer 1

To determine if the point (7, -8) is a solution to the system of inequalities, we need to substitute \(x = 7\) and \(y = -8\) into each inequality and verify if the point satisfies both.

1. **First Inequality:** \(y < \frac{3}{7}x + 7\)

Substitute \(x = 7\) and \(y = -8\):

\[
-8 < \frac{3}{7}(7) + 7
\]

Simplifying the right side:

\[
-8 < 3 + 7
\]
\[
-8 < 10
\]

This is true.

2. **Second Inequality:** \(y \geq -x + 10\)

Substitute \(x = 7\) and \(y = -8\):

\[
-8 \geq -7 + 10
\]

Simplifying the right side:

\[
-8 \geq 3
\]

This is false.

Since the point (7, -8) satisfies the first inequality but does not satisfy the second inequality, the point (7, -8) is **not** a solution to the system of inequalities.