Let the numbers are x and y
and x is larger than y
so, 5 times the larger + 3 times the smaller = 47
So, 5x + 3y = 47
And 4 times the larger - 2 the smaller = 20
so, 4x - 2y = 20
so, we have :
5x + 3y = 47 (1)
4x - 2y = 20 (2)
solve for x and y
Multiply eq.(1) by 2 and eq.(2) by 3
10x + 6y = 94
12x - 6y = 60
Add the last 2 equations:
22x = 154
x = 154/22 = 7
so,
5 * 7 + 3y = 47
3y = 47 - 5*7 = 12
y = 12/3 = 4
So, the numbers are 7 and 4