<PRE><B>Question 633288</B>
3x - y + 4z = 12
x + y - 3z = -4
4x + y - z = 7 
-------------------add the three equations, eliminates z
8x + y = 15
:
Using the 2nd and 3rd equations, multiply the 3rd by -3, add to the 2nd
x + y - 3z = -4
-12x - 3y + 3z = -21
-------------------- adding eliminates z
-11x - 2y = -25
16x + 2y = 30; multiplied 8x+y=15 by 2
---------------adding eliminates y, find x
5x = 5
x = 1
:
Find y
8x + y = 15
8(1) + y = 15
y = 15 -8
y = 7
:
Find z
3x - y + 4z = 12
3(1) - 7 + 4z = 12
-4 + 4z = 12
4z = 12 + 4
z = 16/4
z = 4
:
Summarize
x = 1
y = 7
z = 4
:
:
Check this in the 2nd equation
x + y - 3z = -4
1 + 7 - 3(4) = -4
8 - 12 = -4
:
You can check this in the other two equations</PRE>