Big Ideas Math Integrated I, 2016
BI
Big Ideas Math Integrated I, 2016 View details
7. Systems of Linear Inequalities
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Exercise 2 Page 260

Plot the given points on the coordinate plane with the system of inequalities.

(1,-2), see solution.

Practice makes perfect
Let's plot the given points on the same coordinate plane as the system of inequalities.
system and points

When looking at the four points, the first thing we can notice is that (0,-4) and (-1,-6) lie squarely within the solution set, and the points (1,-2) and (2,-4) rest on the boundary lines. What does it mean when a line is dashed and when it is solid?

  • A solid line tells us that the inequality is not strict. Therefore, the points on the boundary line are solutions to the inequality.
  • A dashed line tells us that the inequality is strict. Therefore, the points on the boundary line are not solutions to the inequality.

With the above in mind, we can conclude that (2,-4) is a solution to the system because it lies on a solid line. However, the point (1,-2), which lies on both a solid and a dashed line, is a solution to one of the inequalities but not to the other. Therefore, (1,-2) does not belong with the others as it's not a solution.