Systems of Inequalities
The systems of inequalities are the set of two or more inequalities with one or more variables. Systems of inequalities contain multiple inequalities with one or more variables.
The system of inequalities is of the form:
a11x1 + a12x2 + a13x3 …….. + a1nxn < b1
a21x1 + a22x2 + a23x3 …….. + a2nxn < b2
an1x1 + an2x2 + an3x3 …….. + annxn < bn
Graphical Representation of Systems of Inequalities
System of inequalities is a group of multiple inequalities. First, solve each inequality and plot the graph for each inequality. The intersection of the graph of all the inequalities represents the graph for systems of inequalities.
Consider an example,
Example: Plot graph for systems of inequalities
- 2x + 3y ≤ 6
- x ≤ 3
- y ≤ 2
Solution:
Graph for 2x + 3y ≤ 6
Shaded region of the graph represents 2x + 3y ≤ 6
Graph for x ≤ 3
Shaded region represents x ≤ 3
Graph for y ≤ 2
Shaded region represents y ≤ 2
Graph for given system of inequalities
Shaded region represents given system of inequalities.
Inequalities
Inequalities are the expressions which define the relation between two values which are not equal. i.e., one side can be greater or smaller than the other. Inequalities are mathematical expressions in which both sides are not equal. They are used to compare two values or expressions. It is a mathematical expression used to compare the relative size or order of two objects or values.
They are fundamental in solving problems in mathematics, economics, engineering, and various other fields.
Inequalities
In this article, we will learn about Inequalities including their symbols, rules/properties, types, and their graphical representations and others in detail.
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