A system of inequalities is a set of two or more inequalities that use the same variables. An inequality is usually denoted as some variable that is greater than, less than, or equal to another variable. These variables are usually denoted as a, b, and so on depending on the amount of variables there are in the system. A system of linear equations is solved when numbers are inserted in place of the variables and you solve for all equations in the system. A TI89 graphing calculator can simplify the process of solving large systems of inequalities to just a few button clicks.
Things You'll Need
 TI89
 System of linear equations
Solving Simple Inequalities

Press "F2" and then press the keypad number "1" on the calculator to access the "Solve" function of the calculator. The word "solve(" should appear on the screen.

Type in the system of inequalities using numbers and letters present on the calculator. In order to reach the common symbols used in inequalities type "2nd," the number "5" and the number "8" to reveal a list that you can scroll down and choose from for your equation.

Type a comma after the inequality.

Type the letter of the variable after the comma and add the closing parentheses for the solve( function.

Press the "Enter" button to solve the inequality. The answer will appear underneath the equation on the screen.
Solving Multiple Inequalities

Divide the inequality by its symbols. This means that you will take everything from the first number through the first inequality symbol until you reach the second inequality symbol, and call it your first inequality. Your second inequality will be the first number or variable after the first inequality symbol until the end of the equation or the next inequality symbol. Repeat until you have divided your multiple inequalities into several simple inequalities.

Type each simple inequality into the calculator using the method from above and solve accordingly.

Record each answer given by the calculator. The variable or variables will be equal to each and every answer. With multiple inequalities, multiple numbers will often solve the inequality, and this is a normal and correct mathematical answer.
References
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