Question

find the value of x and y from the equal ordered pairs:
(2^x+y , 3^x-y ) = (16,9)​

Answer 1

Answer:

Step-by-step explanation:

The sides have a common factor of x+y and so any pair of the form (n,−n), where n is an integer, is a solution.

With that factor out of the picture, we consider

x2−xy+y2=x+y

which can be written as a quadratic in x as

x2−x(y+1)+y2−y=0.

So that x is an integer, we insist that the discriminant is a square. In other words,

m2+3(y−1)2=4

for integer m.

The y-solutions in integers are 2,1,0

giving the following pairs as the remaining solutions

(x,y)=(0,1),(2,1),(1,2),(2,2),(0,0),(1,0) of which (0,0) has already played

Answer 2

Answer:

1) (2^x+y) =(16, 9)

2^x=16

x=4

y=9

2) (3^x-y) =(16, 9)

3^x=16

y=-9