What is a System of Linear Equations?

1
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.
2
3 Ways to Solve Systems of Linear Equations

• Using a Graph to Solve
• Using Substitution
• Using Combination

3
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.
Solve both equations for y, so that each equation
looks like y mx b.
Step 2 Graph both equations on the same
coordinate plane.
Use the slope and y - intercept for each equation
in step 1. Be sure to use a ruler and graph
paper!
Step 3 Estimate where the graphs intersect.
This is the solution! LABEL the solution!
Step 4 Check to make sure your solution makes
both equations true.
Substitute the x and y values into both equations
to verify the point is a solution to both
equations.
4
Y 2x-6 and x-2y6

• Solve by graphing
• Write is slope intercept form ymxb

5
X y -2 and 2x 3y -9

• Solve by graphing
• Write is slope intercept form ymxb

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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.

7
X y -2 and 2x 3y -9

8
Work the Following

• Y -x 3 and y x 1
• Y 2x 4 and y -1/2x 1
• 2x 3y 9 and x -3

9
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.

10
x y -2 2x3y -9

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Work the Following

• Y -x 3 and y x 1
• Y 2x 4 and y -1/2x 1
• 2x 3y 9 and x -3