If 9^2x=22y+1 and 3x-1/2y=61/2.Find the value of x+3y

Answer 1

We start by solving the second equation for x:

3x - (1/2)y = 61/2

Multiplying both sides by 2:

6x - y = 61

Rearranging the first equation:

9^(2x) = 22y + 1

We can rewrite 9 as 3^2:

(3^2)^(2x) = 22y + 1

Using the property (a^b)^c = a^(b*c):

3^(4x) = 22y + 1

Now we can replace 3^(4x) in the equation above with (3^2)^(2x):

(3^2)^(2x) = 22y + 1

3^(2*2x) = 22y + 1

3^(4x) = 22y + 1

Since the left side of the equation is the same, we can equate the right sides:

22y + 1 = 22y + 1

Thus, the equations are dependent, meaning there are infinitely many solutions. As a result, we cannot determine a unique value for x+3y.