Question

Solve the following system of equations.
2x + 2y + z = 10
3x - y + 3z = 10
2x + 3y - 2z = 6

I'm not good at systems of three equations. Anyone willing to help me start?

Answer 1

From what I attempted:
2x+2y+z=10
3x-y+3x=10
I multiplied the bottom equation by negative three and I got the equation:
8x+7z=30 after adding them. Was I supposed to do this first?

Answer 2

Can you tell me what you did to get those two equations?

Answer 3

Also, with those two equations do I use them together to solve for one of the variables?

Answer 4

2x + 2y + z = 10
3x - y + 3z = 10 -->(2)
--------------
2x + 2y + z = 10
6x - 2y + 6z = 20 (result of multiplying by 2)
--------------add
8x + 7z = 30

3x - y + 3z = 10 -->(3)
2x + 3y -2z = 6
-------------
9x - 3y + 9z = 30 (result of multiplying by 3)
2x + 3y - 2z = 6
------------add
11x + 7z = 36

8x + 7z = 30 --->(-1)
11x + 7z = 36
------------
-8x -7z = -30 (result of multiplying by -1)
11x + 7z = 36
-----------add
3x = 6
x = 2

8x + 7z = 30
8(2) + 7z = 30
16 + 7z = 30
7z = 30 - 16
7z = 14
z = 2

2x + 2y + z = 10
2(2) + 2y + 2 = 10
4 + 2y + 2 = 10
2y + 6 = 10
2y = 10 - 6
2y = 4
y = 2

check...
3x - y + 3z = 10
3(2) - 2 + 3(2) = 10
6 - 2 + 6 = 10
12 - 2 = 10
10 = 10 (correct)

x,y,and z, are all 2

Answer 5

Thanks to both of you! I'll use Kellie's work for reference on any more problems, and thanks DSS for starting me off

Answer 6

you have to be really careful with elimination because if you mess up at the beginning, that mistake carries all the way through to the end

Answer 7

Thanks for the advice, it'll help a lot since Elimination is the main form I use to solve these

Answer 8

just remember, whatever variable you eliminate in the first two equation you use, you have to eliminate the same variable in the second set of equations you use.

Answer 9

I would suggest checking your answers at the end to make sure they are correct

Answer 10

okay. By the way, do you know a link to any good Logarithm videos?

Answer 11

no sorry...not really

Answer 12

good luck finding some :) and I am glad I could help with the elimination