f 5 times the first number plus 3 times the second number equals 47, and 10 times the first number minus 4 times the second number equals 54, what are the numbers?

1st number --- x

2nd number --- y

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

double the first:
10x + 6y = 94
10x - 4y = 54
subtract them:
10y = 40
y = 4
back into the first
5x + 3(4) = 47
x = 7