SOLUTION: Please help me solve this equation 4x + 4y + z = 2 -x + 2y + 3z = 5 x + y + 4z = -7

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Question 420741: Please help me solve this equation
4x + 4y + z = 2
-x + 2y + 3z = 5
x + y + 4z = -7
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
4x+4y+1z = 2-------------- 1
-1x +2y+3z =5-------------- 2
1x+ 1y +4z=-7--------------3

consider equation 1 &2
Multiply 1 by 1
Multiply 2 by -2
we get
4 x + 4 y + 1 z = 2
2 x + -4 y + -6 z = -10
Add the two
6 x + 0 y + -5 z = -8 ------------- 4
consider equation 2 & 3
Multiply 2 by 1
Multiply 3 by -2
we get
-1 x + 2 y + 3 z = 5
-2 x + -2 y + -8 z = 14
Add the two
-3 x + 0 y + -5 z = 19 ------------- 5
Consider (4) & (5)
Multiply 4 by 1
Multiply (5) by 2
we get
6 x + -5 z = -8
-6 x + -10 z = 38
Add the two
0 x + -15 z = 30
/ -15
z = -2

Plug the value of z in 5
-3 x + 10 = 19
-3 x = 9
x = -3
plug value of x & z in 1
-12 + 4 y + -2 = 2
4 y = 12 + 2 + 2
4 y = 16
y= 4