Question 236513
okay, call the first number x and the second number y

5x + 3y = 47
10x -4y = 54

So now we have two simultaneous equations.  Double everything in the top equation :

10x + 6y = 94

Now both equations start with a 10x   So take the second equation away from the new top one and the 10x bits will disappear :

(10x - 10x) + 6y - (-4y) = 94 - 54

10y = 40   (because taking away a minus equals a plus)

y = 4

Substituting back into either of the original equations gives x = 7

So the two numbers are 7 and 4.