The sum of two numbers is 15. one number is 7 less then the other. what are the two numbers

One number is 4, the other is 11

Step-by-step explanation:

"The sum of two numbers is 15" can be written as

x + y = 15 where x is one number, and y is the other. Their sum is 15

"one number is 7 less then the other' can be written as

x = y - 7 x is one number that is 7 less than the other

Now we know x = y - 7. We can plug that into the first equation x + y = 15 and solve ...

The first equation is now ...

y - 7 + y = 15 ('x' is substituted for y - 7)

Now solve ...

2y - 7 = 15 (combine like terms)

2y = 22 (add 7 to both sides to isolate the term with the variable)

y = 11 (divide both sides by 2 to isolate the variable)

If y = 11, then

x + 11 = 15 (the 'y' in the first equation becomes 11)

Then x = 4 (subtract 11 from both sides to isolate x)

One is 11 and the other is 4