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

Question

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.