Question

if 3^x-y=9,3^x+y=81 then x,yare​

Answer 1

Answer:

3^x-y=3^2. 3^x+y=3^4

x-y=2. x+y=4

adding both the equation

x-y=2

x+y=4

2x=6

x=3

3+y=4

y=1

Answer 2

$\sf If \: {3}^{x - y} = 9 , {3}^{x + y} = 81 \: then \: \: x = 3 \: and \: y = 1$

Given :

$\sf {3}^{x - y} = 9 \: , \: {3}^{x + y} = 81$

To find : The value of x and y

Solution :

Step 1 of 3 :

Write down the given equations

Here the given equations are

$\sf {3}^{x - y} = 9 \: , \: {3}^{x + y} = 81$

Step 2 of 3 :

Form equations with x and y

$\sf {3}^{x - y} = 9$

$\sf \implies {3}^{x - y} = {3}^{2}$

$\sf \implies x - y = 2 \: \: - - - (1)$

$\sf {3}^{x + y} = 81$

$\sf \implies {3}^{x + y} = {3}^{4}$

$\sf \implies x + y = 4 \: \: \: - - - (2)$

Step 3 of 3 :

Find the values of x and y

x - y = 2 - - - - - - - (1)

x + y = 4 - - - - - - - (2)

Adding Equation 1 and Equation 2 we get

2x = 6

⇒ x = 3

From Equation 1 we get

y = x - 2

⇒ y = 3 - 2

⇒ y = 1

Hence x = 3 , y = 1

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