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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.
(I), (II): x=-3, y=11
(II): a(-b)=-a⋅b
(I), (II): Add and subtract terms
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+83x+y>2
|
{11>-3+83(-3)+11>2
|
{11>5 ✓2>2 ×
|
{y>-x+82x+3y≥7
|
{11>-(-3)+82(-3)+3(11)≥7
|
{11>11 ×27≥7 ✓
|
{y≤-3x+1x−y≥-15
|
{11≤-3(-3)+1-3−11≥-15
|
{11≤10 ×-14≥-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.