SOLUTION: The sum of two numbers is 33. Their difference is 9. What are the two numbers?

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Question 125705: The sum of two numbers is 33. Their difference is 9. What are the two numbers?
Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
1. x%2By=33 : The sum of two numbers is 33
2. x-y=9 : The difference of the same two numbers is 9

Add the two equations, term-by-term:
2x%2B0y=42
2x=42
x=21

Multiply the first equation by -1
-x-y=-33

Add the second equation to this new equation
+0x-2y=-24+
+-2y+=+-+24
+y+=+12+

Check:
21+%2B+12+=+33
21-12+=9

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let numbers be x and y
if the sum of two numbers is 33, we have:
x%2By=33
if their difference is 9, then we have:
x-y=9

to find out what are the two numbers, solve this system:
x%2By=33...........(1)
x-y=9 ............(2)


solve (1) for x
x%2By=33...........(1)
x=+33+-y...........substitute in (2)

%2833+-y%29-y=9 ............solve for y

-y+-y+=+9+-33
-2y+=++-24
y+=++-24%2F-2
y+=++12
then
x=++33-12...........
x=+21...........

check:
x%2By=33...........(1)
21%2B12=33
33+=+33
x-y=9 ............(2)
21-12=9
9=9