SOLUTION: how to write it this promblem The difference of two positive numbers is 10. The larger is twice the smaller decreased by 7. Find the two numbers

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Question 522874: how to write it this promblem
The difference of two positive numbers is 10. The larger is twice the smaller decreased by 7. Find the two numbers
Answer by umail08(87) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = larger number
Let y = smaller number
x – y = 10 … since the difference is positive then you must subtract the smaller from the larger
x = 2y – 7 … larger number is twice the smaller decreased by 7
Solve system of equations:
1) x – y = 10
2) x = 2y – 7
1) x – y = 10
2) x – 2y = -7
Subtract #2 from #1
y = 17
1) x – y = 10
x – 17 = 10
x = 27