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Find the two numbers

The sum of twice a first number and five times a second number is 99. If the second number is subtracted from five times the first number the result is 45. Find the numbers
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1 Answer

Let f be the first number and s the second.
2f+5s=99
5f  -s =45
Multiply the first equation by 5 and the second by 2 to get
10f+25s=495
10f   -2s= 90
Subtract to get
27s=405,  or s=15 and from the second equation 5f=60 or f=12