Question 1042299: Can I please have your assistance? Solve the system : x + y + z = 6, 2x - y + z = 3, x + y - z = 0
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39630)   (Show Source):
Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website! Can I please have your assistance? Solve the system : x + y + z = 6, 2x - y + z = 3, x + y - z = 0
x + y + z = 6 -------- eq (i)
2x - y - z = 3 ------- eq (ii)
x + y - z = 0 -------- eq (iii)
3x = 9 ------- Adding eqs (i) & (ii)
Instead of 2x - y - z = 3, equation (ii) should have been: 2x - y + z = 3 , and so: 
Answer by ikleyn(52884)  (Show Source):
You can put this solution on YOUR website! .
Solve the system : x + y + z = 6, 2x - y + z = 3, x + y - z = 0
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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.
Answer. x = 1, y = 2, z = 3.
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