Question

Is (2, –6) a solution to this system of inequalities?

y
≥
1
2
x
− 7

y ≤ –8

Answer 1

To determine if the point (2, -6) is a solution to the system of inequalities, we will substitute \( x = 2 \) and \( y = -6 \) into both inequalities.

1. For the first inequality:

\[
y \geq \frac{1}{2}x - 7
\]

Substituting \( x = 2 \) and \( y = -6 \):

\[
-6 \geq \frac{1}{2}(2) - 7
\]

Calculating the right side:

\[
-6 \geq 1 - 7
\]
\[
-6 \geq -6
\]

This inequality is **true**.

2. For the second inequality:

\[
y \leq -8
\]

Substituting \( y = -6 \):

\[
-6 \leq -8
\]

This inequality is **false**.

Since the point (2, -6) satisfies the first inequality but does **not** satisfy the second inequality, it is not a solution to the system of inequalities.

Thus, the answer is **no**, (2, –6) is not a solution to this system of inequalities.