The sum of two numbers is 37. The difference
between the two same numbers is 9. Find the
two numbers, listing the larger value first.
Let's call the two numbers x and y.
We know that the sum of the two numbers is 37, so we can write the equation:
x + y = 37
We also know that the difference between the two numbers is 9, so we can write the equation:
x - y = 9
Now we have a system of two equations:
x + y = 37
x - y = 9
We can solve this system of equations by adding the two equations together to eliminate y:
(x + y) + (x - y) = 37 + 9
2x = 46
x = 23
Now that we have x, we can substitute it back into one of the original equations to solve for y:
23 + y = 37
y = 14
So the two numbers are 23 and 14, with the larger value listed first.