Is (0,−3)

Question

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 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 makes both inequalities true.

Answer 1

To determine if (0, -3) is a viable solution for the given system of inequalities, we need to check if the point satisfies both inequalities.

1. First inequality: \( y < -5x + 2 \)

   Substitute \( x = 0 \) and \( y = -3 \): \[ -3 < -5(0) + 2 \] \[ -3 < 2 \] This is true.

2. Second inequality: \( 3y > 3x - 6 \)

   Substitute \( x = 0 \) and \( y = -3 \): \[ 3(-3) > 3(0) - 6 \] \[ -9 > -6 \] This is false.

Since the point (0, -3) satisfies the first inequality but does not satisfy the second inequality, it is not a viable solution for the system.

The correct response is:

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