What is a System of Linear Equations?A system of linear equations is simply two or more linear equations using the same variables.

We will only be dealing with systems of two equations using two variables, x and y.

If the system of linear equations is going to have a solution, then the solution will be an ordered pair (x , y) where x and y make both equations true at the same time.

3 Ways to Solve Systems of Linear Equations

• Using a Graph to Solve

• Using Substitution

• Using Combination

Graphing to Solve a Linear System

Let's summarize! There are 4 steps to solving a linear system using a graph.

Step 1: Put both equations in slope - intercept form.

Step 2: Graph both equations on the same coordinate plane.

Step 3: Estimate where the graphs intersect.

Step 4: Check to make sure your solution makes both equations true.

Solve both equations for y, so that each equation looks like

y = mx + b.

Use the slope and y - intercept for each equation in step 1. Be sure to use a ruler and graph paper!

This is the solution! LABEL the solution!

Substitute the x and y values into both equations to verify the point is a solution to both equations.

Y = 2x-6 and x-2y=6• Solve by graphing

• Write is slope intercept form y=mx+b

X + y = -2 and 2x – 3y = -9• Solve by graphing

• Write is slope intercept form y=mx+b

Steps to Solving by Substitution• Solve one of the equations for one of its

variables.

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

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

• Check the solution in each of the original equations.

X + y = -2 and 2x – 3y = -9

•

Work the Following:

• Y = -x +3 and y = x + 1

• Y = 2x – 4 and y = -1/2x + 1

• 2x – 3y = 9 and x = -3

Steps to Solving by Combinations:

• Arrange the equations with like terms in columns.• Multiply one or both of the equations by a number to

obtain coefficients that are opposites for one of the variables.

• Add the equations from Step 2. Combining like terms will eliminate one variable. Solve for the remaining variable.

• Substitute the value obtained in step 3 into either of the original equations and solve for the other variable.

• Check the solution in each of the original equations.

x + y = -2 2x–3y = -9•

Work the Following:

• Y = -x +3 and y = x + 1

• Y = 2x – 4 and y = -1/2x + 1

• 2x – 3y = 9 and x = -3