# MATH 302 Chapter Notes - Chapter 1.5: Linear Inequality, Free Variables And Bound Variables, Solution Set

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Linear Inequalities

Linear inequality in two variables is simple ax+by <, >, <= or >=, c

You may have a system of linear inequalities,that is you have multiple equations like

these, and you need to find the solution set.

To do this, you look at the answer to each linear inequality and then find the

overlapping answers

Note: If these were not inequalities, but instead equations then if you had two variables,

you may only have been able to solve two equations, or maybe 3 or more, by assuming

one as a free variable.

Anyways, you plot the graph for a linear inequality, this divides the area in two half

planes. Then you look for a test point, on either of the half planes and see if it satisfies

the inequality. That part of the plane is your answer to the inequality.

You do that for all the linear equations, and the overlapping part is your answer.

Also make sure that if the inequality is a simple < or > then you draw a dotted line and if

it has an equals to sign, then your draw a solid line.

This entire process is useful when solving double integrations

Few key terms to make note of are:

Feasible region: The final answer, the overlapping of many areas

Corner point: The intersection of two boundary lines (or I guess more) is the corner

point

Boundary line: The equation plotted on x-y plane

You could go about these problems by breaking down the coordinate system in

individual axis, but that would complicate the problem, as apart from the obvious

solution of one of the axis being greater/lesser than the required number, there is the

problem of the sum/difference of the axis being greater/lesser than the required

number.

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