Table of contents
- 0. Fundamental Concepts of Algebra3h 29m
- 1. Equations and Inequalities3h 27m
- 2. Graphs1h 43m
- 3. Functions & Graphs2h 17m
- 4. Polynomial Functions1h 54m
- 5. Rational Functions1h 23m
- 6. Exponential and Logarithmic Functions2h 28m
- 7. Measuring Angles40m
- 8. Trigonometric Functions on Right Triangles2h 5m
- 9. Unit Circle1h 19m
- 10. Graphing Trigonometric Functions1h 19m
- 11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
- 12. Trigonometric Identities 2h 34m
- 13. Non-Right Triangles1h 38m
- 14. Vectors2h 25m
- 15. Polar Equations2h 5m
- 16. Parametric Equations1h 6m
- 17. Graphing Complex Numbers1h 7m
- 18. Systems of Equations and Matrices3h 6m
- 19. Conic Sections2h 36m
- 20. Sequences, Series & Induction1h 15m
- 21. Combinatorics and Probability1h 45m
- 22. Limits & Continuity1h 49m
- 23. Intro to Derivatives & Area Under the Curve2h 9m
18. Systems of Equations and Matrices
Graphing Systems of Inequalities
Struggling with Precalculus?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Graph the system of inequalities and indicate the region (if any) of solutions satisfying all equations.
3x−2y>6
3x−2y < −4
A
B
C
D

1
Start by rewriting the given inequalities in slope-intercept form (y = mx + b). For the first inequality, 3x - 2y > 6, solve for y to get y < (3/2)x - 3.
For the second inequality, 3x - 2y < -4, solve for y to get y > (3/2)x + 2.
Graph the line y = (3/2)x - 3. Since the inequality is y < (3/2)x - 3, use a dashed line to indicate that points on the line are not included in the solution. Shade the region below this line.
Graph the line y = (3/2)x + 2. Since the inequality is y > (3/2)x + 2, use a dashed line to indicate that points on the line are not included in the solution. Shade the region above this line.
The solution to the system of inequalities is the region where the shaded areas overlap. This is the region between the two lines, not including the lines themselves.