Question

Is (0,−3) a viable solution for the following system? y<−5x+2 3y>3x−6 (1 point) Responses (0,−3) is a nonviable solution since it makes both inequalities true. left parenthesis 0 comma negative 3 right parenthesis is a nonviable solution since it makes both inequalities true. (0,−3) is a viable solution since it makes both inequalities true. left parenthesis 0 comma negative 3 right parenthesis is a viable solution since it makes both inequalities true. (0,−3) is a viable solution since it makes one inequality true. left parenthesis 0 comma negative 3 right parenthesis is a viable solution since it makes one inequality true. (0,−3) is a nonviable solution since it does not make both inequalities true

Answer 1

To determine whether \((0, -3)\) is a viable solution for the system of inequalities given, we need to evaluate both inequalities with \(x = 0\) and \(y = -3\).

1. **First inequality:**
\[
y < -5x + 2
\]
Substituting \(x = 0\) and \(y = -3\):
\[
-3 < -5(0) + 2 \quad \Rightarrow \quad -3 < 2
\]
This is **true**.

2. **Second inequality:**
\[
3y > 3x - 6
\]
Substituting \(x = 0\) and \(y = -3\):
\[
3(-3) > 3(0) - 6 \quad \Rightarrow \quad -9 > -6
\]
This is **false**.

Since \((0, -3)\) makes the first inequality true but the second inequality false, it does not satisfy both inequalities.

Thus, the correct response is:
\[
(0,-3) \text{ is a nonviable solution since it does not make both inequalities true.}
\]