Solving Systems of Linear Equations using elimination

Solving Systems of Linear Equations using elimination

Review.....

Opposites - When placed on a number line, these numbers are the exact same distance away from the 0, but on opposite sides or in opposite directions

Multiple Choice

What is the opposite of 9?

• 9

• 0

• -9

• 18

Additive inverses

Two numbers whose sum is zero

Multiple Choice

What is the additive inverse of 9?

• 9

• 0

• -9

• 18

Multiple Choice

What does 3 + (-3)=

• 6

• -6

• 0

• 3

Multiple Choice

What does 5x + (-5x) =

• 10x

• -10x

• 0

• 5x

Strategies for solving linear systems

Before....

Checking an ordered pair

Graphing and finding the intersection point

Substitution

NOW....

ELIMINATION

Solving Linear Systems by Elimination

Sometimes we can add equations that have two variables to obtain a new equation that only has one variable. In this sense, we are ELIMINATING a variable in order to solve the system

Steps:

1. Add the equations to eliminate one variable
2. Solve the new equation
3. Substitute value found in step 2 into either original equation to find the value of the other variable

Example 1 ....

Solve the linear system by adding the equations

2x + 3y = 11

-2x + 5y = 13

Example 2 ...

Solve the linear system by adding the equations

4x + 3y = 2

5x + 3y = -2

Example 3 ...

Solve the linear system by adding the equations

8x - 4y = -4

4y = 3x + 14

You try....

Solve the linear system of equations. Remember to write your answer as an ordered pair (x,y)

4x - 3y = 5

-2x + 3y = -7

You try....

Solve the linear system of equations. Remember to write your answer as an ordered pair (x,y)

-5x - 6y = 8

5x + 2y = 4