Find x,y,z

Question

2x-3y+z=-1
2x-y+2z=6
5x-4y+3z=6

Please show work I want to learn!!!

Answer 1

http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

x= 1, y=2, z = 3

Answer 2

probably the most method used for 3by3 equations is called elimination
The object is to eliminate one or more variables from pairs of equations.
Usually we look at the coefficents of each variable and choose the one with the smallest or simplest numbers.
In this case it doesn't matter too much.
I will choose the z's

double the first:
4x - 6y + 2z = -2
the second as is
2x - y + 2z = 6
subtract them ---> 2x - 5y = -8 , #4

triple the first:
6x - 9y + 3z = -3
the third as is:
5x - 4y + 3z = 6
subtract them: --> x - 5y = -9 , #5

#4 - #5
x = 1
back in #4
2 - 5y = -8
-5y = -10
y = 2

back in the first:
2 - 6 + z = -1
z = 3

x=1 , y=2, z=3

check by subbing those values into the original 3 equations,
(it works!)

There are many ways I could have gone here.
We were lucky that both y terms in #4 and #5 were the same
Had they been opposite, I would have added the equations
Had both the x's and y's been different, I would have to multiply each equation by some value so that they would be the same

Answer 3

thanks