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

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.

#x+y−2z=5#
#−x+2y+z=2#
#2x+3y−z=9#

1 Answer
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

1
Feb 9, 2018

Answer:

#x=1#, #y=2# and #z=-1#

Explanation:

Given the system:

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

We can eliminate #z# from the first equation by adding twice the second equation to it to get:

#-x+5y=9#

We can eliminate #z# from the second equation by adding the third equation to it to get:

#x+5y=11#

We can eliminate #y# from this last equation by subtracting the previous equation to get:

#2x = 2#

Then we can divide both sides by #2# to find:

#color(blue)(x = 1)#

We can substitute this value of #x# into the previous equation to find:

#1+5y = 11#

Subtracting #1# from both sides, we get:

#5y = 10#

Then dividing both sides by #5# we find:

#color(blue)(y = 2)#

Substituting these values for #x# and #y# into the second equation we were given, we find:

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

That is:

#3+z = 2#

Subtracting #3# from both sides, we find:

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

Was this helpful? Let the contributor know!
1500
Impact of this question
41 views around the world
You can reuse this answer
Creative Commons License