2x+y+4z=12, 8x-3y+2z=20, 4x+11y-z=33 solve by gauss elimination method
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Given : 2x+y+4z=12, 8x-3y+2z=20, 4x+11y-z=33
To Find : Solve for x , y & z
Solution:
2x+y+4z=12 Eq1
8x-3y+2z=20 Eq2
4x+11y-z=33 Eq3
Eq2 + 2 Eq3
=> 8x - 3y + 8x + 22y = 20 + 66
=> 16x + 19y = 86
Eq1 + 4 Eq3
=> 2x+y+ 16x + 44y = 12 + 132
=> 18x + 45y = 144
16x + 19y = 86 Eq4
18x + 45y = 144 Eq5
8 * Eq5 - 9 Eq4
=> 189y = 378
=> y = 2
=> 16x+ 19(2)= 86
=> 16x = 48
=> x = 3
x = 3
y = 2
2x+y+4z=12
=> 6 + 2 + 4z = 12
=> z = 1
x = 3 , y = 2 , z = 1
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