SOLUTION: X+2y+z=7 X+3z=11 2x-3y=1

Question 983164: X+2y+z=7
X+3z=11
2x-3y=1

Found 2 solutions by Timnewman, ankor@dixie-net.com:
Answer by Timnewman(323) (Show Source): You can put this solution on YOUR website!
Call, x+2y+z=7---(1)
x+3z=11----(2)
2x-3y=1----(3)
from equ (1)
z=7-2y-x----(4)
substitute equ (4) in equ (2)
x+3(7-2y-x)=11
clear the bracket and get
x+3y=5----(5)
dd equ (3) and (5)
3x=6
divide bothsides by 3
3x/3=6/3
x=2.
from equ 3
y=(1-2x)/(-3)----(6)
put x=2 in equ 6
y=(1-2(2)/(-3)
y=(1-4)/(-3)
y=-3/(-3)
y=1
put the value of x and y in equ 4
z=7-2(1)-2
z=7-2-2
z=7-4
z=3
the value of x,y,z is 2,1,3 respectively.
HOPE THIS HELPS,,,,,
BEST REGARD
___TIMNEWMAN
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
X + 2y + z = 7
X + 3z = 11
2x - 3y = 1
:
Use elimination here, multiply the 3rd equation by -1 and add
X + 2y + z = 7
X + 0y + 3z = 11
-2x + 3y + 0 = -1
-------------------Addition eliminates x
5y + 4z = 17
4z = -5y + 17
divide by 4
z = -1.25y + 4.25
:
Use elimination again on the 1st two equation
X + 0y + 3z = 11
X + 2y + z = 7
----------------subtraction eliminates x again
-2y + 2z = 4
simplify divide by 2
-y + z = 2
z = y + 2
:
z = z, therefore
y + 2 = -1.25y + 4.25
y + 1.25y = 4.25 - 2
2.25y = 2.25
y = 1
then
z = 1 + 2
z = 3
Find x using x + 3z = 11
x + 3(3) = 11
x = 11 - 9
x = 2
:
we have x=2; y=1; z=3
:
Check that in the 1st equation: x + 2y + z = 7, replace xyz
2 + 2(1) + 3 = 7

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