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 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 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 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.

Answer 1

To determine if (0, −3) is a viable solution for the system of inequalities, we need to plug in x = 0 and y = -3 into both inequalities and see if they hold true.

1. **First Inequality:**
\( y < -5x + 2 \)
Plugging in (0, -3):
\[
-3 < -5(0) + 2 \\
-3 < 2 \quad \text{(True)}
\]

2. **Second Inequality:**
\( 3y > 3x - 6 \)
Plugging in (0, -3):
\[
3(-3) > 3(0) - 6 \\
-9 > -6 \quad \text{(False)}
\]

Since (0, -3) satisfies the first inequality but does not satisfy the second inequality, we can conclude that:

**(0,−3) is a nonviable solution since it does not make both inequalities true.**