Linear Inequalities in Two Variables

Explain in Detail :Graphical Solution of Linear Inequalities in Two Variables

A graphical solution is a way of solving linear inequalities in two variables using a graph. To graphically solve a linear inequality in two variables, you will need to plot the points representing the inequality and then connect the points with a line. The line will be the solution to the inequality.

The following steps will show you how to graphically solve a linear inequality in two variables:

1. Plot the points representing the inequality.

2. Connect the points with a line.

3. Draw a shading pattern on the line to indicate the solution to the inequality.

The following examples will show you how to graphically solve linear inequalities in two variables.

Example 1: Graph the inequality x < 2

To graph the inequality x < 2, you will need to plot the points (0,0) and (1,1).

Then, connect the points with a line and draw a shading pattern on the line to indicate the solution to the inequality. The following graph illustrates the solution to the inequality x < 2.

Example 2: Graph the inequality y ≥ 2

To graph the inequality y ≥ 2, you will need to plot the points (0,0) and (2,2).

Then, connect the points with a line and draw a shading pattern on the line to indicate the solution to the inequality. The following graph illustrates the solution to the inequality y ≥ 2.

Different Types of Linear Inequalities

There are three types of linear inequalities:

1) Absolute value inequalities

2) Linear inequalities in one variable

3) Linear inequalities in two variables

Solved Example of Linear Inequalities with Two Variables

The following example illustrates how to solve a linear inequality with two variables.

x + 2y ≤ 6

To solve a linear inequality with two variables, we use the following steps:

Step 1: Isolate the variable we want to solve for.

In this example, we want to solve for y.

x + 2y ≤ 6

x + 2y – x = 6 – x

y = 6 – x

Step 2: Plug in the value for y that we found in Step 1 into the inequality.

If y = 3, then

x + 2(3) ≤ 6

x + 6 ≤ 6

x ≤ 0