Algebra 2Solving systems of Linear Equations and

Systems of Linear Inequalities

Lee Ellen McCallEDET 640/Fall 2010

TI-84 Plus Graphing Calculator Tutorial

S. C. State StandardIA-2: The student will demonstrate through

the mathematical process an understanding of functions, systems of equations, and systems of linear inequalities.

IndicatorsIA-2.1 Carry out a procedure to solve a

system of linear inequalities algebraically (simultaneous inequalities).

IA-2.2 Carry out a procedure to solve a system of linear inequalities graphically.

IA-2.11 Carry out a procedure to solve a system of equations.

Solving Systems of Simultaneous Inequalities Algebraically

When solving systems of simultaneous inequalities:

Step 1: Solve each inequality separatelyStep 2: Find the common values between the

two inequalities.Example: Solve and graph the following

simultaneous inequalities.

x + 2 < 6 and x – 3 > -16 < 2 – 3x < 14

Your Turn!Now it’s your turn! Pause the tutorial while

you practice solving and graphing systems of simultaneous inequalities algebraically.

1.-4 < 6x – 10 ≤ 142.3x + 5 ≤ 11 or 5x -7 ≥ 233.-5 < x + 1 < 4

Solving Systems of Linear Inequalities Graphically

The easiest way to solve systems of linear inequalities is graphing. Let’s look at how we solve these by hand and then we will solve the same system using our graphing calculator.

Step 1: Graph each inequality in the system. Remember to shade the solution set.

Step 2: Identify the region that is common to all graphs.

Example: y > -2x - 5 and y ≤ x + 3These are in the y-intercept form, so we will graph

their similar equations.

y = -2x – 5 and y = x + 3

Your TurnNow it’s your turn! Pause the tutorial while

you practice solving systems of inequalities using your TI-84 Plus.

1.y – x ≤ 3 and y ≥ x + 22.y < -x -3 and x > y – 23.3x + 2y ≤ 6 and 4x – y < 2

Solving Systems of Linear Equations Algebraically

Two Methods

1.Substitution- In the substitution method, one equation is solved for one variable in terms of the other. Then, this expression is substituted into the other equation.

Step 1: Solve one of the equations for one of its variables.

Step 2: Substitute the expression from Step 1 into the other equation and solve for the other variable.

Step 3: Substitute the value from Step 2 into the revised equation from Step 1 and solve.

Solving Systems of Linear Equations AlgebraicallyElimination- In the elimination method, compare the

coefficients of each variable and manipulate the coefficients to eliminate one of the variables.

Step 1: Multiply one or both of the equations by a constant to obtain coefficients that differ only in sign for one of the variables.

Step 2: Add the revised equation from Step 1. Combining like terms will eliminate one of the variables. Solve for the remaining variable.

Step 3: Substitute the value obtained in Step 2 into either of the original equations and solve for the other variable.

ExamplesLet’s look at an example using both methods.

2x = 5y = -5x + 3y = 3

Your TurnNow it’s your turn! Pause the tutorial while

you practice solving systems of equations algebraically. Use either method to solve the practice problems.

1. 12x – 3y = -9 3. 8x + 9y = 15 -4x + y = 3 5x – 2y = 17

2. 6x + 15y = -12 -2x – 5y = 9

Using the TI-84 Plus……..Now, let’s solve the same equations using the

TI-84 Plus graphing calculator.

The EndThank you for using this educational tutorial.