Question 126227: solve the system by addition method. if a unique solution doesn't exist, state whether the system is inconsistent or dependent.
2x-3y+z=5
x+4y-2z=-3
4x-2y+3z=6
I could really use some. I am pulling out my hair. Please.
Answer by uma(370)   (Show Source):
You can put this solution on YOUR website! 2x-3y+z=5 -----------(1)
x+4y-2z=-3 -------------(2)
4x-2y+3z=6 --------------(3)
(2) + (1)*2 gives, 5x - 2y = 7 ------------(4)
(1)*3 - (3) gives, 2x - 7y = 9 -------------(5)
Now the equationsa are reduced to 2 in 2 variables.
(4) * 2 gives, 10x - 4y = 14
(5) * 5 gives, 10x - 35y = 45
Subtracting the above 2 equations, we get, 31 y = - 31
==> y = -1
Plugging this in (4) gives, 5x + 2 = 7
==> 5x = 7 - 2
==> 5x = 5
==> x = 1
Substituting x = 1, y = -1 in (1) , 2 + 3 + z = 5
==> 5 + z = 5
==> z = 5 - 5
==> z = 0
Thus x = 1, y = -1, z = 0
Good luck!!!
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