Question

1. which ordered pair is a solution of the system of linear inequalities shown?

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$$\begin{cases} 2x + 3y > 12 \\\\ x - y \\leq 1 \\end{cases}$$

(0, 4)
(5, 2)
(6, 0)
(0, 5)

Explanation:

Step1: Test (0, 4)

Substitute \(x = 0\), \(y = 4\) into \(2x + 3y > 12\): \(2(0)+3(4)=12\), not \(>12\). So (0,4) is out.

Step2: Test (5, 2)

Substitute into \(2x + 3y > 12\): \(2(5)+3(2)=10 + 6 = 16>12\). Substitute into \(x - y \leq 1\): \(5 - 2 = 3\leq1\)? No. So (5,2) is out.

Step3: Test (6, 0)

Substitute into \(2x + 3y > 12\): \(2(6)+3(0)=12\), not \(>12\). So (6,0) is out.

Step4: Test (0, 5)

Substitute into \(2x + 3y > 12\): \(2(0)+3(5)=15>12\). Substitute into \(x - y \leq 1\): \(0 - 5=-5\leq1\). Both inequalities hold.

Answer:

(0, 5)