How to Solve Systems of Linear Inequalities
Systems of linear inequalities are a little harder to solve than linear equalities. However, the basic principles are the same. Instead of having a set intersection point as your solution, you will have a solution set, which is represented graphically. With a little practice, solving systems of linear inequalities will become much easier.
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Instructions
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1
Write down your system of inequalities.
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2
Solve and graph each inequality separately. Solve each inequality for x or y. Remember to be consistent and solve for the same variable in all each inequality in the system.
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3
Create a table of values for each inequality. You will normally need at least three points. Choose three values for y for each inequality. Substitute the values into your solved inequalities to determine your points. Remember points are written in the form (x, y).
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4
Graph each individual line. Use the points you found in Step 3.
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5
Determine where to shade for each line. Choose a point above or below each line and substitute into the inequality belonging to the line. If the point makes the inequality true, then lightly shade the side of the line containing that point. If the point makes the inequality false, shade the opposite side of the line.Repeat the process for each line.Your final solution is the darkest shaded area, or the shaded portion all three lines share.
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Tips & Warnings
You can choose to solve for either x or y.
If fractions result when solving an inequality, try to use values in your table of values that will cancel out the fraction.
Remember that inequalities with < or > will use a dotted line on the graph.
Remember that inequalities with ≤ or ≥ will use a solid line on the graph.
When choosing a test point for shading, never choose a point on any of your lines.
Always try to shade areas lighter than your lines to avoid confusion.
