Solving Linear Systems

1
Solving Linear Systems

• Substitution Method
• Lisa Biesinger
• Coronado High School
• Henderson,Nevada

2
Linear Systems

• A linear system consists of two or more linear
  equations.
• The solution(s) to a linear system is the ordered
  pair(s) (x,y) that satisfy both equations.

3
Example

• Linear System
• The solution will be the values for x and y that
  make both equations true.

4
Solving the System

• Step 1 Solve one of the equations for either x
  or y.
• For this system, the first equation is easy to
  solve for x because the coefficient of x is equal
  to 1.

5
Organizing Your Work

• Set up 2 columns on your paper.
• Place one equation in each column.
• Write the equation we are using first in column
  1, and the other equation in column 2.

6
Solving by Substitution

• Now we will solve for x in column 1.

7
Solving by Substitution

• Subtract 2y from both sides.

8
Solving the System

• Step 2 Substitute your answer into the other
  equation in column 2.
• Substituting will eliminate one of the variables
  in the equation.

9
Solving by Substitution

• Always use parenthesis when substituting an
  expression with two terms.

10
Solving the System

• Step 3 Simplify the equation in column 2 and
  solve.

11
Solving by Substitution

• Use the distributive property and combine like
  terms.

12
Solving by Substitution

• Solve for y.

13
Solving the System

• Step 4 Substitute your answer in column 2 into
  the equation in column 1 to find the value of the
  other variable.

14
Solving by Substitution

• Substitute for y and solve for x. Solve for x.

15
The Solution

• The solution to this linear system is
• and .
• The solution can also be written as an ordered
  pair

16
Almost FinishedChecking Your Solution

• Check your answer by substituting for x and y in
  both equations.

17
Checking Your Answer

• ?

• ?

18
Additional Examples

• Answers
• 1
• 2
• 3

• Problem 1
• Problem2
• Problem 3