SOLUTION: 3x-5y+z=10 2x+2y-z=12 5x+3y-2z=15

Question 908138: 3x-5y+z=10
2x+2y-z=12
5x+3y-2z=15
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
3 x + -5 y + z = 10 -------------- 1
2 x + 2 y - z = 12 -------------- 2
5 x + 3 y + -2 z = 15 -------------- 3

consider equation 1 &2 Eliminate y
Multiply 1 by 2 -5
Multiply 2 by 5 4
we get
6 x + -10 y + 2 z = 20
10 x + 10 y + -5 z = 60
Add the two
16 x + 0 y + -3 z = 80 ------------- 4
consider equation 2 & 3 Eliminate y
Multiply 2 by 3
Multiply 3 by 2
we get
6 x + 6 y + -3 z = 36
10 x + 6 y + -4 z = 30
Add the two
16 x + 12 y + -7 z = 66 -------------5 5
Consider (4) & (5) Eliminate x
Multiply 4 by 1
Multiply (5) by -1
we get
16 x + -3 z = 80
-16 x + 7 z = -66
Add the two
4 z = 14
/ 4
z = 3 1/ 2
16 x -7 z= 66
16 x -24 1/ 2 = 66
x = 5 21/32
Plug x & z in eq (1)
3x-5y +z=10 --------------1
16 31/32-5y + 3 1/ 2 = 10
-5y= -10 15/32
y =2 3/32
x= 5 21/32 y= 2 3/32 z= 3 1/ 2

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