Let x = first number
Let y = second number

>>...5 times the first number plus three times the second number equals 47...<<

That says

>>...5 times x + 3 times y = 47...<<

Or 5x + 3y = 47

>>...10 times the first number minus 4 times the second number equals 54...<<

That says:

>>...10 times x minus 4 times y = 54...<<

Or 10x - 4y = 54

So you have the system of equations:



Can you solve that?  If not, post again asking how.

Answer:  first number = 7, second number = 4

Edwin