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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
