The given point $(- 3, 11)$ is a solution to a system of inequalities if it satisfies every inequality in the system. Let's substitute the point into the given systems one at a time until we find the correct one.

Option A

If the given point satisfies both inequalities at the same time, the point is a solution to the system. Let's substitute the point into both inequalities of the system.

{y \geq x - 2 2 x + y \leq 5 (I) (II)

$(I), (II):$ $x = - 3$ , $y = 11$

⎩ ⎪ ⎨ ⎪ ⎧ 11 \geq ? - 3 - 2 2 (- 3) + 11 \leq ? 5

MultPosNeg

$(II):$ $a (- b) = - a \cdot b$

⎩ ⎪ ⎨ ⎪ ⎧ 11 \geq ? - 3 - 2 - 6 + 11 \leq ? 5

$(I), (II):$ Add and subtract terms

{11 \geq - 5 ✓ 5 \geq 5 ✓

Because we obtained true statements from both inequalities by substituting the point

(- 3, 11),

it is a solution to the system in option A.

Checking the Remaining Options

Although option A is correct, let’s verify our answer by checking the remaining options as well. To do so, we will following the same procedure for each of the remaining systems.

System	Substitution	Simplify
${y > x + 8 3 x + y > 2$	${11 > - 3 + 8 3 (- 3) + 11 > 2$	${11 > 5 ✓ 2 > 2 \times$
${y > - x + 8 2 x + 3 y \geq 7$	${11 > - (- 3) + 8 2 (- 3) + 3 (11) \geq 7$	${11 > 11 \times 27 \geq 7 ✓$
${y \leq - 3 x + 1 x - y \geq - 15$	${11 \leq - 3 (- 3) + 1 - 3 - 11 \geq - 15$	${11 \leq 10 \times - 14 \geq - 15 ✓$

When we substitute the point $(- 3, 11)$ into any of the remaining systems, at least one of the inequalities is not satisfied. Therefore, the point $(- 3, 11)$ is not a solution of any of the remaining systems. This means that, as we discovered at the beginning of our solution, the correct answer is indeed option A.

Exercise