Linear Inequalities in Two Variables A linear inequality is an inequality that involves variables raised to the power of 1 or lower. It can be used to d...
Linear Inequalities in Two Variables
A linear inequality is an inequality that involves variables raised to the power of 1 or lower. It can be used to describe situations where a certain quantity must fall within a certain range of values.
Linear inequalities can be written in the form of:
a1x + a2y ≤ b
a1x + a2y ≥ b
a1x - a2y ≤ b
a1x - a2y ≥ b
where a1, a2, b are constants.
Properties of Linear Inequalities:
A linear inequality is always true when the inequality symbol is reversed.
A linear inequality is true if and only if the corresponding linear equation is true.
A linear inequality is equivalent to a linear equation if and only if the two expressions are equal.
Solving Linear Inequalities:
To solve a linear inequality, we need to isolate the variable on one side of the inequality symbol. We can do this by performing the same operations on both sides of the inequality, such as adding, subtracting, multiplying, or dividing both sides by the same constant.
Examples of Linear Inequalities:
2x + 3y ≤ 10
4x - y ≥ 1
3x - 2y ≤ 6
Applications of Linear Inequalities:
Linear inequalities are used in various applications, including:
Optimization problems
Inequalities in economics
Inequalities in physics
Inequalities in engineering