Question

Solve the following system of equations:

2x + 2y + z = 10
3x − y + 3z = 10
2x + 3y − 2z = 6

Answer 1

use the elimination method
start off by multiply the 3rd equation by -1 and add it to the first equation
this will eliminate x

Answer 2

2x + 2y + z = 10
-2x- 3y+ 2z = -6 add
y + 3z = 4

Answer 3

all 3 of them?

Answer 4

no - now get another equation in y and z using the second and third equations

Answer 5

multiply second equation by -2
and third equation by 3

then add

Answer 6

sorry gotta go

Answer 7

okay thank you

Answer 8

I still don't get it . . . .

Answer 9

how do I use the elimination one

Answer 10

first take 2 of the 3 equations...any 2.. and eliminate a variable
2x + 2y + z = 10 --->(-1)
2x + 3y - 2z = 6
---------------
-2x - 2y - z = -10 (result of multiplying by -1)
2x + 3y - 2z = 6
---------------add
y - 3z = -4

are you still with me...do you have any questions so far ?

Answer 11

im here

Answer 12

once you find that number where do you put it? back in the x?

Answer 13

now we take 1 of the equations we used and he one we did not use, and eliminate the same variable
2x + 2y + z = 10 --->(3)
3x - y + 3z = 10 --->(-2)
--------------
6x + 6y + 3z = 30 (result of multiplying by 3)
-6x + 2y - 6z = -20 (result of multiplying by -2)
-------------add
8y - 3z = 10

still following me ? any questions so far ?

Answer 14

now we take our results from the equations we did..and eliminate a variable
y - 3z = -4 --->(-1)
8y - 3z = 10
-----------
-y + 3z = 4 (result of multiplying by -1)
8y - 3z = 10
-------------add
7y = 14 -- divide both sides by 7
y = 2

still there ? any questions so far ?

Answer 15

okay

Answer 16

now since we have found y, we sub it back into one of the equations we have already eliminated the x from.
y - 3z = -4
2 - 3z = -4
-3z = -4 - 2
-3z = -6 -- divide both sides by -3
z = 2

understand so far ?

Answer 17

now that we have found y and z, we sub those back into one of the original equations to find x.
2x + 2y + z = 10
2x + 2(2) + 2 = 10
2x + 4 + 2 = 10
2x + 6 = 10
2x = 4
x = 2

but before you turn in these answers, lets check them
2x + 3y - 2z = 6
2(2) + 3(2) - 2(2) = 6
4 + 6 - 4 = 6
6 = 6 (correct)

so x = 2, y = 2, and z = 2

It is not really that hard...just very time consuming. And if you mess up at the beginning of the problem, it follows you all the way to the end. That is why it is always best to check your answers.

Answer 18

ANY questions at all ?

Answer 19

look over this real well and if you have any questions, just tag me :)

Answer 20

Thank you so much! it really helped me you deserve a medal :)