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Question 498889: please help solve this three linear equation containing three unknowns
x-3y+z=13
3x+y-4z=13
-4x-4y+2z=0
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! please help solve this three linear equation containing three unknowns
x-3y+z=13
3x+y-4z=13
-4x-4y+2z=0
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Solving for z in the 3rd equation gives:
z = 2x + 2y
Substitute this value into the other two equations:
x - 3y + (2x + 2y) = 13 -> 3x - y = 13 [1]
3x + y - 4(2x + 2y) = 13 -> -5x - 7y = 13 [2]
Solve for y in [1], substitute into [2]:
y = 3x - 13
-5x - 7(3x - 13) = 13
Simplify and solve for x:
-5x - 21x + 91 = 13
-26x = -78
x = 3
From above, y = 3*3 - 13
y = -4
Therefore z = 2*3 + 2*-4
z = -2
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