Question

Is (0,−3) a viable solution for the following system?

y<−5x+2

3y>3x−6

(1 point)
Responses

(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 nonviable solution since it does not make both inequalities true.
left parenthesis 0 comma negative 3 right parenthesis is a nonviable solution since it does not make both inequalities true.

(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 one inequality true.
left parenthesis 0 comma negative 3 right parenthesis is a viable solution since it makes one inequality true.

Answer 1

To determine if the point \((0, -3)\) is a viable solution to the system of inequalities, we need to test it in both inequalities:

1. The first inequality is:
\[
y < -5x + 2
\]
Substituting \(x = 0\) and \(y = -3\):
\[
-3 < -5(0) + 2
\]
This simplifies to:
\[
-3 < 2
\]
This statement is true.

2. The second inequality is:
\[
3y > 3x - 6
\]
Substituting \(x = 0\) and \(y = -3\):
\[
3(-3) > 3(0) - 6
\]
This simplifies to:
\[
-9 > -6
\]
This statement is false.

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

Therefore, the correct response is:
\((0,−3)\) is a nonviable solution since it does not make both inequalities true.