Solve systems of linear inequalities by graphing calculator

A system of linear inequalities is a set of two or more linear inequalities.

We can solve a system of linear inequalities by graphing each inequality and identifying where the shaded areas overlap.

If you’d like to review how to graph a linear inequality, check out our

lesson!

If we imagine that the shaded area for each inequality represents safety from a specific monster, then the space where all the shaded areas overlap represents the area we’re completely safe and contains the solutions to the system of inequalities.

Select the safe Brains. If none are safe, just press Check!

Remember, a solid line means the boundary is also safe, and a dotted line means the boundary is not safe.

How do we check if a point is a solution to a system of linear inequalities?

We can plug in the and values of the point into each linear inequality and simplify.

If all of the inequalities simplify to a true statement, then the point is a solution.

Point: ✅

If one or more of the inequalities simplify to a false statement, then the point is not a solution.

Point: ❌

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Equations in which the unknown only appear to the first power are called linear equations. The general form of a linear equation in one variable is ax + b = 0, where x is the variable.

A linear inequality resembles an equation by replacing the equal sign with an inequality symbol. Generally, a range of values, rather than one specific value will be the solution to a linear inequality. Some of the examples of Linear Inequation are listed below.

• x < 7
• 5 - y ≥ 30
• x + 5 > 20
• Q ≠ 50

Steps for Linear Inequalities Graphing

The linear inequality graph intersects the coordinate plane into two parts by a borderline. In order to plot the graph of an inequality, we have to follow some basic steps:

• Firstly, check if the given linear inequality equation is arranged properly or not.
• If not rearrange the equation, where the variable will be on the left side and the rest of the expression on the right side of the inequality symbol
• In this step, put the x values in the equation and plot the graph.
• Retain to draw a solid line for y≤ or y≥ and a dashed line for y< or y>.
• Finally, shade the line as per inequalities, like above the line for a “greater than” (y> or y≥) and below the line for a “less than” (y< or y≤).

Steps for Solving One Variable Linear Equations and Inequations

To solve the linear equation or inequality having only one variable, the steps provided below are followed to balance the equation:

• Firstly, add or subtract like terms
• Isolate the variable
• Reverse or eliminate the terms
• Check the answer.

Example:

Find inequality for 6x + 4 > 28

Solution:

Put the variable on the LHS and reverse all the other terms or the coefficient of x to the RHS.

6x > 28 - 4

6x > 24

 ⇒ x > 4

Hence, the value of x is greater than 4.

Go through all the topics of linear equations from our reliable website ie., Linearequationscalculator.com, and find free online calculators related to linear equations and inequalities concepts.

Example: 2x+3>23

Example (Click to try)

2x+3>23

How to solve your inequality

To solve your inequality using the Inequality Calculator, type in your inequality like x+7>9.
The inequality solver will then show you the steps to help you learn how to solve it on your own.

Less Than Or Equal To

Type <= for "less than or equal to". Here is an example:
4x+3<=23

Greater Than Or Equal To

Type >= for "greater than or equal to". Here is an example:
5x+3>=23

Solving Inequalities Video Lesson

• Khan Academy Video: Solving Inequalities

Need more problem types? Try MathPapa Algebra Calculator

How do you solve systems of linear inequalities by graphing?

How do you solve systems of linear inequalities?

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