27x/81^x-2y =9, x+4y=0
To solve this system of equations, we'll use the substitution method.
From the second equation, we can solve for x in terms of y:
x = -4y.
Plugging this into the first equation, we have:
27(-4y) / 81^(-4y-2y) = 9.
Simplifying, we have:
-108y / 81^(-6y) = 9.
Dividing both sides by -108, we get:
y / 81^(-6y) = -1/12.
Multiplying both sides by 81^6y, we have:
y = (-1/12)(81^6y).
Using exponent rules, we can rewrite this as:
y = (-1/12)(1 / 81^(-6y)).
Multiplying both sides by 12, we have:
12y = -1 / 81^(-6y).
Flipping the fractions on the right-hand side, we have:
12y = -81^6y.
Dividing both sides by -81^6y, we get:
12y / -81^6y = -1.
Simplifying, we have:
-12 / 81^6 = -1.
Cross-multiplying, we have:
-12 = -81^6.
Taking the sixth root of both sides, we have:
81 = 3.
This is not possible; there is an error in the calculations.
Please double-check the equations and try again.