Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
7. Systems of Linear Inequalities
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Exercise 3 Page 260

Graph the point and check if it's within the shaded area.

No

Practice makes perfect

We are asked to determine whether the point (- 4, 3) is the solution of the given system of inequalities. First, let's recall what it means for a point to be a solution of a system of inequalities. If a point is a solution of a system of inequalities, the point is a solution of every inequality in the system. If we represent the system graphically, it means that the point is part of the shaded region.

system

Now, let's graph the ordered pair (- 4,3) and the given system of inequalities on the same coordinate plane. If the ordered pair lies within the shaded area, it is a solution of the system.

system and ordered pair

The given point lies on a solid line, which means that it is a solution of the inequality represented by this line. However, since the point lies outside of the shaded area, it can not be a solution of the second inequality. The ordered pair (- 4,3) is not a solution of the system.