Solving Systems with Elimination Day 1

Solving Systems with Elimination Day 1

Open Ended

 $y=2x\ and\ 3x+2y=28$ Solve the following system of equations using substitution:

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The opposite of -1 is

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The opposite of 14x is

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What is -14x + 14x?

Elimination

• We can eliminate things if, when we add them together, they equal 0.

• Elimination means that we temporarily get rid of one variable.

• Since one variable is gone, we can solve for the other.

• Plug that variable back in to get the variable that got eliminated.

Open Ended

Do you have any questions about elimination so far?

For now...

• we will only be looking at examples that already have opposites. Your job is to...

• Identify the opposite terms

• Add the equations together

• solve for one variable

• solve for the other variable

• put the solution in (x,y)

Multiple Choice

 $10x+4y=150$   $-10x+6y=200$  
Which variable should be eliminated? 

• x

• y

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 $x-y=11$   $2x+y=19$  
Solve the system using elimination.

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 $4x+8y=20$   $-4x+2y=-30$  

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 $-6x+5y=1$   $6x+4y=-10$  

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 $-8x+y=-17$   $7x-y=14$  

Multiple Choice

 $7x-10y=28$   $7x-3y=28$  
Notice that neither variable can be eliminated as is. Just by looking at these equations, which variable do you THINK will be easier to eliminate?

• x

• y

Open Ended

 $7x-10y=28$   $7x-3y=28$  
What has to change so that we can eliminate x?

Open Ended

 $7x-10y=28$   $7x-3y=28$  
What can I multiply one of the x's by to get -7?

Multiple Choice

 $7x-10y=28$   $7x-3y=28$  
If I multiply the bottom equation by -1, what does the new equation look like?

•  $-7x-3y=28$  

•  $-7x+3y=28$  

•  $-7x+3y=-28$  

Fill in the Blanks

 $7x-10y=28$   $-7x+3y=-28$  
Find the solution