Question

Is (1, 2) a solution to this system of inequalities?

4x + y >= 6

4x + 3y > 10

Answer 1

To determine if the point \( (1, 2) \) is a solution to the system of inequalities, we will substitute \( x = 1 \) and \( y = 2 \) into each inequality and check if the inequalities hold true.

1. **First Inequality: \( 4x + y \geq 6 \)**
\[
4(1) + 2 \geq 6
\]
\[
4 + 2 \geq 6
\]
\[
6 \geq 6 \quad \text{(True)}
\]

2. **Second Inequality: \( 4x + 3y > 10 \)**
\[
4(1) + 3(2) > 10
\]
\[
4 + 6 > 10
\]
\[
10 > 10 \quad \text{(False)}
\]

Since the point \( (1, 2) \) satisfies the first inequality but does not satisfy the second inequality, it is not a solution to the system of inequalities.

In conclusion, \( (1, 2) \) is **not** a solution to the system of inequalities.