SOLUTION: Solve this system of equations: 6x+2y+4z=2 3x+4y-8z=-3 -3x-6y+12z=5

Question 907663: Solve this system of equations:
6x+2y+4z=2
3x+4y-8z=-3
-3x-6y+12z=5
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
6 x + 4 y + 2 z = 2 --------------1
3 x + 4 y -8 z = -3 --------------2
-3 x + -6 y + 12 z = 5 --------------3

consider equation 1 &2 Eliminate y
Multiply 1 by -1 -5
Multiply 2 by 1 4
we get
-6 x + -4 y + -2 z = -2
3 x + 4 y + -8 z = -3
Add the two
-3 x + 0 y + -10 z = -5 ------------- 4
consider equation 2 & 3 Eliminate y
Multiply 2 by 3
Multiply 3 by 2
we get
9 x + 12 y + -24 z = -9
-6 x + -12 y + 24 z = 10
Add the two
3 x + 0 y + 0 z = 1 -------------5 5
Consider (4) & (5) Eliminate x
Multiply 4 by 1
Multiply (5) by 1
we get
-3 x + -10 z = -5
3 x + 0 z = 1
Add the two
0 x + -10 z = -4
/ -10
z = 2/ 5
3 x + 0 z= 1
3 x + 0 = 1
x = 1/ 3
Plug x & z in eq (1)
6 x + 4 y + 2 z = 2 --------------
2 + 4 y + 4/ 5 = 2
4 y = - 4/ 5
y = - 1/ 5
x= 1/ 3 y= - 1/ 5 z= 2/ 5

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