Question

The number of solutions of 3 x+y = 243 and 243x-y = 3 is
(a) 0 (b) 1 (c) 2 (d) infinite​

Answer 1

b) 1 will be the answer

Step-by-step explanation:

here

a1/a2 is not equal to b1 /b2

so it has only one solution .

hope it will help you .

Answer 2

The correct answer to the following question is (b)

Given: equation 1, $3^{x+y}$ = 243

           equation 2, $243^{x-y}$ = 3

To find: Number of solution

Solution:

Equation 1 is $3^{x+y}$ 243

Equation 2 is $243^{x-y}$ = 3

Now,  $3^{x+y}$= 243

        , $3^{x+y}$ = 3⁵

Therefore, x+y = 5 →(i)

Now, $243^{x-y}$ = 3

       , $3^{5(x-y)}$ = 3

Therefore, 5(x-y) = 1

               , x - y = 1/5 → (ii)

Now adding both the equation

(x+y) - (x-y) = 5 + 1/5

2y = 26/5

y = 26/10 = 13/5

Now putting the value of y in equation (i)

x+13/5 = 5

x = 5 - 13/5

x = 12/5

Therefore, the value of x = 12/5 and y = 12/5

Since only one pair of solution are there,

Therefore, the number of solution is 1

So, the correct option is (b).