Question

question 4
is the origin in the solution area for this system of inequalities below?
y ≥ -\frac{5}{3}x - 3
y ≥ -\frac{1}{3}x + 1
\bigcirc yes, (1, 0) is included in the solution area.
\bigcirc no, (0, 0) is not included in the solution area.
\bigcirc yes, (0, 0) is included in the solution area.
\bigcirc no, (1, 0) is not included in the solution area

Explanation:

Step1: Test origin in first inequality

Substitute \(x = 0\), \(y = 0\) into \(y\geq-\frac{5}{3}x - 3\).
Left side: \(0\). Right side: \(-\frac{5}{3}(0) - 3 = -3\).
Check \(0\geq - 3\): True.

Step2: Test origin in second inequality

Substitute \(x = 0\), \(y = 0\) into \(y\geq-\frac{1}{3}x + 1\).
Left side: \(0\). Right side: \(-\frac{1}{3}(0) + 1 = 1\).
Check \(0\geq 1\): False.

Since the origin fails the second inequality, it is not in the solution area.

Answer:

No, (0, 0) is not included in the solution area.