Substitute the given point into the given systems.
A
Practice makes perfect
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.
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 3x+y > 2
11 > - 3+8 3( -3)+ 11 > 2
11 > 5 ✓ 2 > 2 *
y > - x+8 2x+3y ≥ 7
11 > - ( -3)+8 2( -3)+3( 11) ≥ 7
11 > 11 * 27 ≥ 7 ✓
y≤ -3x+1 x-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.
