Question

1. which of the following would be a possible solution to the system of inequalities given below?

\

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

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

Explanation:

Step1: Test (0,4) in inequalities

First inequality: $2(0)+3(4)=12$, not $>12$ → fails.
Second inequality: $0-4=-4 \leq 1$ → passes, but overall invalid.

Step2: Test (5,2) in inequalities

First inequality: $2(5)+3(2)=10+6=16 > 12$ → passes.
Second inequality: $5-2=3 \leq 1$ → fails, overall invalid.

Step3: Test (6,0) in inequalities

First inequality: $2(6)+3(0)=12$, not $>12$ → fails.
Second inequality: $6-0=6 \leq 1$ → fails, overall invalid.

Step4: Test (0,5) in inequalities

First inequality: $2(0)+3(5)=15 > 12$ → passes.
Second inequality: $0-5=-5 \leq 1$ → passes, overall valid.

Answer:

(0, 5)