Solving Systems of Linear Inequalities Adapted from Walch
Education
Slide 3
Key Concepts A system of inequalities is two or more
inequalities in the same variables that work together. The solution
to a system of linear inequalities is the intersection of the half
planes of the inequalities. Look for the area where the shading of
the inequalities overlaps; this is the solution.
Slide 4
Practice # 1 Solve the following system of inequalities
graphically:
Slide 5
Graph the line x + y = 10. Use a dashed line because the
inequality is non-inclusive Shade the solution set. First pick a
test point. Choose a point that is on either side of the line. Test
point: (0, 0) Since the point (0, 0) makes the inequality false,
shade the opposite side of the line.
Slide 6
Graph the line 2x 4y = 5 on the same coordinate plane. Use a
dashed line because the inequality is non-inclusive Shade the
solution set. First pick a test point. Choose a point that is on
either side of the line. Test point: (0, 0) Since the point (0, 0)
makes the inequality false, shade the opposite side of the
line.
Slide 7
The overlap of the two shaded regions, which is darker,
represents the solutions to the system: