How do you find the solution region for the system of linear inequalities?

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The easiest way is graphically. 

Linear inequalities can be represented by areas above or below straight lines. Plot the lines by replacing the inequality with equals. Use the inequality to decide whether it’s the area above or below the linear plots. The equations of the lines should be expressed in the form y=mx+a so that mx+a>0, for example, is the area above the line, while mx+a<0 is the area below. The areas include the lines themselves for ≥ or ≤. Compound equalities are represented by the area between two parallel lines. For example, -1<x<3 would be represented by the area between x=-1 and x=3.

After shading the relevant areas, parts of the areas will overlap. Where this happens all the inequalities involved are satisfied simultaneously. The overlap defines the required region. 

 

by Top Rated User (1.1m points)

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