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 half-plane is below/shaded the line

• Equation iii) 5x - 3y ≤ 15

• Slope: 5/3

• Y-intercept: 5

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

• Shade/half-plane 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.