Question 1042299
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Solve the system : x + y + z = 6, 2x - y + z = 3, x + y - z = 0
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<pre>
 x + y + z = 6,    (1)
2x - y + z = 3,    (2)
 x + y - z = 0     (3)

Add equations (2) and (3) (both sides). You will get

3x = 3.   Hence, x = 1.

Substitute x = 1 into equations ((1) and (3). You will get

1 + y + z = 6,
1 + y - z = 0,

or, which is the same,

y + z =  5,    (3)
y - z = -1.    (4)

Now add the equations (3) and (4) (both sides). You will get

2y = 4.   Hence, y = 2.

Now from (3) z = 5 - y = 5 - 2 = 3.

<U>Answer</U>.  x = 1,  y = 2,  z = 3.
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