Linear Inequality In Two Variables
Linear Inequality in Two Variables
How to remember each concept:
Solving linear equations in two variables:
 Linear equation in two variables.
 Use substitution or elimination to solve
Graphing linear inequalities in two variables:
 Graph the boundary line by finding x and y intercepts
 Use test point on either side to shade appropriate half plane
Half plane:
 A half plane is a region on a plane that is bounded by a line.
Types of linear equations in two variables:

Equation i) x + 2y > 5

Slope: 1/2

Y intercept: 5/2

Graph as solid line as equation is ‘>’

Half plane is the region is above/shaded the line.

Equation ii) 3x + 4y < 6

Slope: 3/4

Y intercept: 3/2

Graph the line as a solid line since the equation is ‘<’.

The shaded halfplane is below/shaded the line

Equation iii) 5x  3y ≤ 15

Slope: 5/3

Yintercept: 5

Graph the line as a solid line as the inequality sign is ‘≤’

Shade/halfplane is below/on the line.
Finding the feasible region of a system of linear inequalities:
 Graph all the inequalities
 Feasible region is area that satisfies all the inequalities
Applications of linear inequalities, including optimization problems:
 Optimization problems find maximum or minimum values of function
Linear programming
 Linear programming: optimize (maximize or minimize) linear function subject to linear inequality constraints.
Solving linear inequalities involving absolute values:
 Graph separately.
 Find union of the two graphs.