Question

2x+3y-z=9, x+y+z=9, 3x-y-z=-1 find the gaussin elimination method.​

Answer 1

Given:

2x+3y-z=9, x+y+z=9, 3x-y-z=-1

To find:

The solution of the given equation

Solution:

We have given the equation as:

2x+3y-z=9------------(I)

x+y+z=9 -------------(II)

3x-y-z=-1 -----------(III)

on Adding eq (I) and (II) we get

2x+3y-z=9

x+y+z  = 9  

3x + 4y = 18-----------------------(IV)

on Adding eq (II) and (III) we get

x+y+z=9

3x-y-z=-1

4x   = 8

x = 8/4

x = 2

Now put the value of x in eq (IV)

3x+4y = 18

• 6+4y = 18
• 4y = 18-6
• 4y = 12
• y = 3

Now put the value of x and y in eq (II)

x+y+z = 9

• 2+3+z = 9
• 5+z = 9
• z = 9-5
• z = 4

Hence the solution of the given system is (2, 3, 4)