Verified answer

a) x + 2y - z = 4

b) 3x - y + 2z = 3

c) -x + 3y + z = 6

Add equations (a) and (c):

x + 2y - z = 4

-x + 3y + z = 6

________________

5y = 10

y = 10/5 = 2

substitute y = 2 into equations (b) and (c), multiply equation (c) by 3, add the equations:

3x - 2 + 2z = 3

3x + 2z = 5

-x + 3(2) + z = 6

-x + z = 0

-3x + 3z = 0

3x + 2z = 5

-3x + 3z = 0

______________

5z = 5

z = 5/5 = 1

substitute values for y and z into equation (a):

x + 2(2) - 1 = 4

x + 3 = 4

x = 1

check by substituting values for x, y and z into equation (b):

3(1) - 2 + 2(1) = 3

3 = 3

So x = 1, y = 2, z = 1

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OK

Key is to get this to two variables. Here is how we start:

x + 2y -z =4

3x -y + 2z = 3

-x +3y +z = 6

First equation -- x = 4 -2y + z

Substitute in the third one

-4+2y-z +3y +z = 6

5y = 10

y = 2

Now back to the first substitution: x = 4 -2(2) + z

x = 4 - 4 +z

x = z

Now go to the second equation

3z -2 +2z = 3

5z = 5

z= 1 and since x = z , x = 1

So the answer is x =1, y=2 and z=1.

Prove it:

1 + 2(2) -1 = 4 ??

4=4 YES!!

3(1) -2 +2(2) = 3

3 = 3 YES!!

-1 + 3(2) + 1= 6??

6 = 6 YES!!

Hope that helps.

x + 2y - z = 4 .......(i)

3x - y + 2z = 3........(ii)

-x + 3y + z = 6 ........(iii)

Add (i) and (iii)

5y=10 or y = 2 .....(iv)...............Ans

3 times (i) -(ii)

3(x + 2y - z) -(3x - y + 2z )= 12-3

3x+6y-3z -3x +y -2z = 9

7y-5z =9 ...........(v)

14 -5z = 9

z= 1..........(vi).....Ans

Put in (i)

x +4 -1 =4

x = 1..........Ans