Example 1

Author:
Walch Education
Solve the following system of inequalities graphically.
  1. Graph the first inequality. Use a dashed line because the inequality is non-inclusive (greater than).
  2. Shade the solution set. First pick a test point. Choose a point that is on either side of the line.
  3. Then, substitute that point into the inequality. If the test point makes the inequality true, shade the region that contains that point. If the test point makes the inequality false, shade on the opposite side of the line. The shaded region represents the solutions for the first inequality.
  4. Graph the second inequality on the same coordinate plane. Use a dashed line because the inequality is non-inclusive (greater than).
  5. Shade the solution set. First pick a test point. Choose a point that is on either side of the line.
  6. Then, substitute that point into the second inequality. If the test point makes the inequality true, shade the region that contains that point. If the test point makes the inequality false, shade on the opposite side of the line. The shaded region represents the solutions for the second inequality.
  7. Find the solutions to the system. The overlap of the two shaded regions, which is darker, represents the solutions to the system.
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