Question 679648: need help solving linear equation in three variables using the elimination method.
-3x-2y+4z=-5
2x+5y-3z=3
4x-y+7z=15
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! They are trying to torment you here, the solutions are not integers!
-3x -2y + 4z =-5
2x + 5y - 3z = 3
4x - y + 7z = 15
:
Multiply the 1st equation by -1 and add
3x + 2y - 4z = 5
2x + 5y - 3z = 3
4x - y + 7z = 15
--------------------adding eliminates z
9x + 6y = 23
:
use the first two original equations, mult the 1st by 3, the 2nd by 4
-9x - 6y + 12z = -15
8x + 20y -12z = 12
--------------------adding eliminates z
-x + 14y = -3
:
the above equation by 9, add to the 1st "two unknown" equation
-9x + 126y = -27
9x + 6y = 23
------------------adding eliminates x find y
132y = -4
y = 4/132 = -1/33, -.0303 as a decimal
:
Find x using 9x + 6y = 23
9x + 6(-1/33) = 23
9x + (-6/33) = 23
9x + (-2/11) = 23
9x = 23 + 2/11
9x = 253/11 + 2/11
9x = 255/11
x = 1/9 * 251/11 = 255/99, 2.576 as a decimal
:
Find z using 4x - y + 7z = 15,
use decimals, here, avoid these disgusting fractions
4(2.576) - (-.0303) + 7z = 15
10.303 + .0303 + 7z = 15
10.333 + 7z = 15
7z = 15 - 10.333
7z = 4.667
z = 4.667/7
z = .6666, which is 2/3 if you insist on fractions
:
Summarize this mess: x = 2.576, y = -.0303, z = .667
:
You can confirm this in the original equations, if you are totally bored with life.
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