SOLUTION: I'm trying to understand my daughters homework. This is one if her word problems I need help breaking down so that I can help her. Thank you much. The sum of two

Question 565278: I'm trying to understand my daughters homework. This is one if her word problems I need help breaking down so that I can help her. Thank you much.
The sum of two mumbers is 15 less than twice the first number. Their difference is 5 less than twice the second number. Find each of the numbers.
Found 2 solutions by mananth, solver91311:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let first number be x
second number be y
x+y = 2x-15
x-y = 2y-5

x+y = 2x-15
-2x
x-2x+y=2x-2x-5
y-x=-15.....................(1)
x-y = 2y-5
-2y
x-y-2y=2y-2y-5
x-3y=-5....................(2)
add equation (1) & (2)
y-3y=-15-5
-2y=-20
/-2
y=10
plug y in (1)
10-x=-15
-x=-10-15
-x=-25
/-1
x=25
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let represent the first number and let represent the second number.

The sum of the two numbers is:

and twice the first number less 15 is:

and since "is" means "equals" we can say:

Similarly, the difference is:

And 5 less than twice the second number is:

Giving us:

Collect terms in each:

Leaving you with a nice little 2X2 system that is all set up to solve by the elimination method.

John

My calculator said it, I believe it, that settles it

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