The larger of two numbers is eight more than the smaller number. the sum is twenty two. find the numbers.

Let's call the larger number a and the smaller number b.
a + b = 22
a - 8 = b
Since we have determined that a - 8 is the same as b, we can substitute it into the original equation:
a + (a - 8) = 22
2a - 8 = 22
2a = 30
a = 15
Now that we have the larger number, let's find the smaller number:
15 - 8 = b
7 = b
Let's see if this is true:

15 + 7 = 22
22 = 22

Da numbers are x and y
x>y

larger is 8 more than smaller
x=8+y

sum is add so
x+y=22
sub 8+y=x

8+y+y=22
8+2y=22
2y=14
y=7

sub back
8+y=x
8+7=x
15=x
da numbers are 7 and 15