Three times the larger of two numbers is equal to four times the smaller the sum of the numbers is 21 find the numbers

Lets x and y are 2 unknown numbers
3x=4y
x + y = 21 so x = 21 - y
replace x = 21 - y into 3x = 4y

3x = 4y
3(21 - y) = 4y
63 - 3y = 4y
63 = 7y
y = 63/7
y =9

x = 21 - y
x = 21-9
x =12

answer 
the numbers are 9 and 12

double check
sum of the numbers is 21 find the numbers = 9 + 12 =21

Three times the larger of two numbers is equal to four times the smaller
3x=4y
3(12) = 4(9)
36 = 36