This set of problems is about the systems of:
- two linear inequalities
- three linear inequalities
- four linear inequalities
The solid lines and the dashed lines are the loci of the points that satisfy the corresponding equalities.
The region where a given inequality holds true is indicated in black text.
The region where two or more inequalities hold true is indicated in yellow text.
Different color shades of the other regions simply indicate that different sets of corresponding inequalities apply to those regions.
Constructing the graphs of these inequalities requires at least two points for each of the corresponding equalities. After plotting, another two points on each side of the plotted line should be tested for the given inequality.
For those of you who want to draw the graphs the old fashioned way (that is, the paper-and-pencil method), finding the points can be a tedious task. This is where spreadsheet formulas can be a lot useful: you use spreadsheet formulas to calculate the points for you. So if you're unfamiliar with those spreadsheet formulas you might want to read my coming blog on simple spreadsheet formulas for calculating the x and y coordinates of points for a given linear equation.
Systems of Two Linear Inequalities
1. Draw the graph of the given system of inequalities:- 3x - 2y > -2
- x + 3y < 5
2. Sketch the graph of the following system:
- 3x - 4y < 2
- 5x - y < 9
3. Sketch the graph of the following system:
- x + 2y > -4
- 3x + y < 3
Systems of Three Linear Inequalities
1. Draw the graph of the given system of inequalities:- 2x + 3y > -2
- x - 4y > -1
- 5x + 2y < 17
2. Draw the graph of the given system of inequalities:
- x - 2y < -7
- 2x - y < 4
- x + y < 2
3. Sketch the graph of the following system:
- 3x - 5y < 7
- 4x - y > -2
- x + 4y > -9
System of Four Linear Inequalities
1. Draw the graph of the given system of inequalities:- 3x - 2y > -13
- 2x + 3y < 6
- x - 3y < 12
- x + 6y > -21
