Systems Elimination Method

Solving systems by 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

Solving Systems by Elimination

Do you see the additive inverse in this problem?

Multiple Choice

What should we do next to solve for the x coordinate of the point?

• Get x by itself by subtracting 3.

• Cry

• Additive Inverse

• Divide both sides by 3 to make a ghost one.

Fill in the Blanks

What is the value of x?

Multiple Choice

If x = 6, we can substitute a 6 in for x. Which x can we replace with 6?

• Only the 2x

• Only the single x

• Only the 3x

• Any x in the problem because the lines cross at a shared x value.

Solving Systems of Linear Equations using elimination

2x - y = 2

x + y = 7​

EXAMPLE

​What if we don't have a graph.

Solving by Elimination

​identify if it is the "x" or the "y" variable that will be eliminated

If the variable to be eliminated is the same - subtract the equations

If the variable to be eliminated is opposite- add the equations

Multiple Choice

Solve by elimination:
4x+4y=4

3x+4y=10

• (7,-6)
• (-6,7)
• (6,7)
• (7,6)

Multiple Choice

Solve by elimination:

3x+7y=23

-3x-7y=-17

• No solution

• (0, 3)

• (-3,3)

• (3,3)

Multiple Choice

Solve by elimination:
4x+9y=28
-4x-y=-28

• (-7,0)
• (6,0)
• (-6,0)
• (7,0)