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Question

If 3x+y=81 and 81xy=3, then find the values of x and y

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Solution

3x+y=81 and 81xy=3

3x+y=34 and 34(xy)=31

Equating the terms with the same bases, we have

x+y=4......(i)

4x4y=1......(ii)

On multiplying eq.(i) by 4 and adding the result to eq.(ii), we get

4x4y+(4x+4y)=1+16

8x=17

x=178

Put x=178 in eq.(i) we get

178+y=4

y=4178=158

x=178,y=158


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