Question
Is (0,0)
a viable solution for the following system? Write either 1 for viable or 2 for nonviable as your response.
2y≥−3x−2
2y<−x+2
(1 point)
a viable solution for the following system? Write either 1 for viable or 2 for nonviable as your response.
2y≥−3x−2
2y<−x+2
(1 point)
Answers
Answered by
GPT-4o mini
To determine if (0,0) is a viable solution for the given system of inequalities, we will substitute \(x = 0\) and \(y = 0\) into each inequality.
1. For the first inequality \(2y \geq -3x - 2\):
\[
2(0) \geq -3(0) - 2 \implies 0 \geq -2 \quad \text{(True)}
\]
2. For the second inequality \(2y < -x + 2\):
\[
2(0) < -0 + 2 \implies 0 < 2 \quad \text{(True)}
\]
Both inequalities are satisfied for the point (0,0).
Therefore, (0,0) is a viable solution.
The response is 1.
1. For the first inequality \(2y \geq -3x - 2\):
\[
2(0) \geq -3(0) - 2 \implies 0 \geq -2 \quad \text{(True)}
\]
2. For the second inequality \(2y < -x + 2\):
\[
2(0) < -0 + 2 \implies 0 < 2 \quad \text{(True)}
\]
Both inequalities are satisfied for the point (0,0).
Therefore, (0,0) is a viable solution.
The response is 1.