How to solve this Algebra Equation?

 13x + 3y = 113  - Original
  8x  +9y = 137.50 - Original

-3(13x) + 3y = 113  Want to multiply by -3 to cancel out the ys
 -39 x  - 9y  = -339
   8x   + 9y  = 137.5
-31x = -201.5  Divide by -31
x = 6.5

Okay, so we know 1 junior ticket is $6.50 Now we solve for the other

13(6.5) + 3y = 113 Solve for y
84.5 + 3y = 113 Move 84.5 to the other side by subtraction
3y = 28.5  Divide by 3
y = 9.5

So lets check it in the other equation!
8(6.5) + 9(9.5) = 137.50
52 + 85.5 = 137.50
137.50

It checks!!

13J+3A=$113
8J+9A=$137.50


 We can increase or decrease the equations
If we do it equally on both sides of the equal sign.

Looking at the equations, we look for simple variable relations

J[13,8]
A[3,9]
A looks simple ,lets Eliminate A

(-3)(13J+3A)=113
(-39J-9A)=339

now we Add the Two equations together to eliminate A.
For J;  (-39+8)=(-31)
For A; (-9+9)=0
......... (-339+137.50)=(-201.50)

showing again.
(-39J-9A)=(-339)
8J+9A=137.50
(-31J+0A)=(-201.50)

J=(-201.50/-31)
J=6.5

Good now we have solved J = $6.50  

Enter the value of J into the original equations.

13*6.50+3A=$113
84.50+3A=113
3A=113-84.50
3A=28.50
A=28.50/3
A=$9.50

Now confirm our answer.

8*6.50+9*9.50=$137.50
52+85.50=137.50

Good!

Adults=$9.50
Junior=$6.50