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Question 916973: 4x+y+3z=11
2x-3y+2z=9
x+y+z=-3
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! 4 x + 1 y + 3 z = 11 -------------- 1
2 x -3 y 2 z = 9 -------------- 2
1 x + 1 y + 1 z = -3 -------------- 3
consider equation 1 &2 Eliminate y
Multiply 1 by 3 -5
Multiply 2 by 1 4
we get
12 x + 3 y + 9 z = 33
2 x -3 y + 2 z = 9
Add the two
14 x 0 y + 11 z = 42 ------------- 4
consider equation 2 & 3 Eliminate y
Multiply 2 by 1
Multiply 3 by 3
we get
2 x -3 y + 2 z = 9
3 x + 3 y + 3 z = -9
Add the two
5 x + 0 y + 5 z = 0 -------------5 5
Consider (4) & (5) Eliminate x
Multiply 4 by -5
Multiply (5) by 14
we get
-70 x -55 z = -210
70 x + 70 z = 0
Add the two
0 x + 15 z = -210
/ 15
z = -14
5 x + 5 z= 0
5 x + -70 = 0
x = 14
Plug x & z in eq (1)
4 x + 1 y + 3 z = 11 -------------- 1
56 + 1 y -42 = 11
1 y = -3
y = -3
x= 14 y= -3 z= -14
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