Solve for x, y and z?
#(5xy)/(x+y)=6#
#(4xz)/(x+z)=3#
#(3yz)/(y+z)=2#
3 Answers
Explanation:
Given:
#{ ((5xy)/(x+y) = 6), ((4xz)/(x+z) = 3), ((3yz)/(y+z) = 2) :}#
Multiplying both sides of the first equation by
#{ (5 = 6(1/x)+6(1/y)), (8 = 6(1/x)+6(1/z)), (9 = 6(1/y)+6(1/z)) :}#
Replacing the last two equations with the result of subtracting the third equation from the second we get:
#{ (5 = 6(1/x)+6(1/y)), (-1 = 6(1/x)-6(1/y)) :}#
Then adding these two equations, we get:
#4 = 12(1/x)#
Hence
Then:
#6(1/y) = 5-6(1/x) = 5-2 = 3#
Hence
Then:
#6(1/z) = 9-6(1/y) = 9-3 = 6#
Hence
See below.
Explanation:
Making
and eliminating
and solving for
Explanation:
We have,
Similarly,
Then,
Altogether,
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