There are 2 numbers. twice the first number minus the second number equals 18. twice the second number minus the first number equals 9. find the numbers.

First, set up the two different equations.

f=first number 
s=second number 
2f - s = 18 
2s - f = 9 

Second, solve the equations by multiplication which will cancel out the s's.  
2(2f - s = 18) 
1 (2s - f = 9)


4f -2s = 36 
2s - f = 9     

4f - f = 45
3f = 45 
f = 15 

So the first number is 15. 

Plug 15 into one of the equations to find the second number. 
2f - s = 18 
2(15) - s = 18
30 - s = 18 
-s = -12 
s = 12 

Overall, the first number is 15 and the second number is 12.

Check:
2f - s = 18 
2(15) - 12 = 18 
30 -12 = 18
18 = 18 True 

2s - f = 9  
2(12) - 15 = 9 
24 - 15 = 9 
9 = 9 True