Answer:
(x, y) = (-7, 11)
Explanation:
The system of exponential equations can be solved by the use of logarithms. Equivalently, the equations can be written so that exponents can be equated. This system is equivalent to two linear equations.
First equation:
2^(x+y) = 16
2^(x +y) = 2^4 . . . . use the same base to write the constant
x +y = 4 . . . . . . . . equate exponents of 2 (take log₂ of both sides)
Second equation:
2^(2x +y) = 1/8
2^(2x +y) = 2^(-3) . . . . use the same base to write the constant
2x +y = -3 . . . . . . equate exponents of 2
Solve the linear equations:
We can subtract the first equation from the second to get ...
(2x +y) -(x +y) = (-3) -(4)
x = -7
y = 4 -x = 4 -(-7) = 4 +7 = 11 . . . . use the first equation to find y
The solution to the system is (x, y) = (-7, 11).