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Question 43140: x+y+z=-3
2x+5y+2z=-12
-x+9y-3z=-11
Answer by psbhowmick(878)   (Show Source):
You can put this solution on YOUR website! The equations to be solved are:
x + y + z = -3 _____(1)
2x + 5y + 2z = -12 ____(2)
-x + 9y - 3z = -11 ____(3)
To solve 3 simultaneous equations in 3 unknowns our objective should be to eliminate any one unknown in order to obtain 2 simultaneous equations in 2 unknowns. To achieve this end, here, we shall eliminate 'x' between all the 3 equations.
Substituting the value of 'x' from (1) in (2) eliminates 'x' between (1) and (2) thus giving the new equation
2(-3 - y - z) + 5y + 2z = -12
or -6 - 2y - 2z + 5y + 2z = -12
or 3y = -12 + 6 = -6
or y = -6/3 = -2 _________(4)
Adding (1) and (3) eliminates 'x' between (1) and (3) thus giving the new equation
(y + z) + (9y - 3z) = -3 + (-11)
or 10y - 2z = -14
or 5y - z = -7 [dividing both sides by 2]
or z = 5y + 7 __________(5)
Substituting the value of 'y' from (4) in (5) we get the value of 'z'
z = 5(-2) + 7 = -10 + 7 = -3
Putting y = -2 and z = -3 in (1) we have
x - 2 - 3 = -3
or x = 2
Thus, the reqd. solution is x = 2, y = -2 and z = -3.
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