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Question

Find the value of m for equarion x+y=18m if x and y satisfying following equations
x+4y=27xy
x+2y=21xy.Find the value of m

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Solution

x+4y=27xy
=>x+4y27=xyx+2y=21xy
=>x+2y=21(x+4y27)
=>x+2y=7(x+4y9)
=>x+2y=7x+28y9
=>9x+18y=7x+28y
=>2x=10y
=>x=5yx+4y=27xy
=>5y+4y=27×5y×y
=>9y=27×5y2
=>y=927×5=115x+4y=27xy
=>x+415=27x×115
=>x+415=9x5
=>15x+4=27x
=>12x=4
=>x=13x+y=1m
=>13+115=1m
=>1m=1845
=>m=45

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