# How does one go about using the elimination method to solve an equation?

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I would love a step by step process please! I just can't seem to understand it the way i was taught. *Thank you!!!*

Here is an example:

Solve the system using the elimination method.

#x+y−2z=5#

#−x+2y+z=2#

#2x+3y−z=9#

I would love a step by step process please! I just can't seem to understand it the way i was taught. *Thank you!!!*

Here is an example:

Solve the system using the elimination method.

##### 1 Answer

#### Answer

#### Answer:

#### Explanation

#### Explanation:

#### Answer:

#### Explanation:

Given the system:

#{ (x+y-2z=5), (-x+2y+z=2), (2x+3y-z=9) :}#

We can eliminate

#-x+5y=9#

We can eliminate

#x+5y=11#

We can eliminate

#2x = 2#

Then we can divide both sides by

#color(blue)(x = 1)#

We can substitute this value of

#1+5y = 11#

Subtracting

#5y = 10#

Then dividing both sides by

#color(blue)(y = 2)#

Substituting these values for

#-(1)+2(2)+z = 2#

That is:

#3+z = 2#

Subtracting

#color(blue)(z = -1)#

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