Question

if 3^x+y=81 and 9^x-y=3 then find x and y​

Answer 1

Answer:

x=7/4    and y=5/4

Expaination:

3^x+y=81 and 9^x-y=3

3^(x+y)=3^3            ______(i)

3^2(x-y)=3              ______(ii)

if base same then the power also same

therefore, x+y = 3      _____(iii)

similarly from equation (ii)

2(x-y)=1   __(there no power on 3 means the power is 1) ____(iv)

2(x-y)=1

=> 2x-2y=1      _____(v)

multiply (iii) by 2

we get  2x+2y=3     ______(vi)

Now, by adding equation (vi) and (v)

we get,

x=7/4

Now put x value n equation (iii)

wet get the value of y

y=5/4