What is 3^{x+y}=81,3^{y-x}=9 ?

The solution to 3^{x+y}=81,3^{y-x}=9 is

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3^{x+y}=81,3^{y-x}=9

3^{x + y} = 81, 3^{y - x} = 9

(x = 1, y = 3)

Solution steps

[3^{x + y} = 81 3^{y - x} = 9]

Isolate

x

for

3^{x + y} = 81 : x = 4 - y

Plug the solutions

x = 4 - y

into

3^{y - x} = 9

For

3^{y - x} = 9

, subsitute

x

with

4 - y : y = 3

Plug the solutions

y = 3

into

3^{x + y} = 81

For

3^{x + y} = 81

, subsitute

y

with

3 : x = 1

Verify solutions by plugging them into the original equations

Therefore, the final solution for

3^{x + y} = 81, 3^{y - x} = 9

(x = 1, y = 3)

2 x + y = 7, x + 2 y = 1

\frac{x}{7} + \frac{y}{3} = 5, \frac{x}{7} - \frac{y}{9} = 1

x + 12 = 1, 2 y^{7} = x - 3

x - 2 y = 3, 2 x + 3 y = 27

2 x - 5 y + 4 = 0, 2 x + 4 - 8 = 0