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Question

can you help me solve this linear equation

2x –y + z = 3
x –2y + z = -4
x + y – z = 3

Answer 1

njk

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Answer 2

Several approaches can be used. One is called Gauss Jordan elimination, another converts the equations to an augmented matrix which is then row reduce. I don't know the level of maths you are studying so the following is the method of elimination as used for two simultaneous equations.

(a) 2x-y+z = 3
(b) x-2y+z = -4

Subtract (b) from (a) to eliminate z and obtain: x + y = 7

Now take:

(b) x-2y+z = -4
(c) x+y-z= 3

Add (b) to (c) to eliminate z and obtain: 2x -y = -1

Hence w we have:

(d) x+y = 7
(e) 2x -y = -1

Add (d) to (e) to eliminate y and obtain: 3x = 6, hence x = 2

Substitute for x in (d): 2+y = 7, hence y = 5

Now substitute x = 2 and y = 5 in (a),(b) or (c):

2*2-5+z = 3

-1+z = 3, hence z = 4

Check for (b) and (c)

2- 2*5+ 4 = -8+4 = -4 as required.

2+5- 4 = 3 as required.

Hence we have:

x = 2, y=5 and z =

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Answer 3

use Gaussian Elimination http://en.wikipedia.org/wiki/Gaussian_elimination

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