Question

The pair of equation 3^x+y=81,81^x-y=3. Find the value of x and y​

Answer 1

Answer:

first equation is,

${3}^{x + y} = 81 = {3}^{4}$

$= x + y = 4$

second equation is,

${81}^{x - y} = 3$

$= { 3}^{4(x - y)} = 3$

$= 4(x - y) = 1$

$x - y = \frac{1}{4}$

Now,

$x + y + x - y = 4 + \frac{1}{4} = \frac{17}{4}$

$= 2x = \frac{17}{4}$

$= x = \frac{17}{8}$

$so \: \: \: y = 4 - \frac{17}{8} = \frac{15}{8}$

Answer 2

Answer:

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