SOLUTION: Name the property that justifies each statement. 1. If x+y=7 and x-y=13, then 2x=20. Please help, I have notes but they do not explain how to find this out.

Question 818367: Name the property that justifies each statement.
1. If x+y=7 and x-y=13, then 2x=20.
Please help, I have notes but they do not explain how to find this out.
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Unclear your steps since you showed or stated no steps done.

What if you added x-y to both sides of the "7" equation?
(x+y)+(x-y)=7+(x-y)
x+y+x-y=7+(x-y)
2x=7+(x-y)
Now check what is (x-y). It was given as a value in the "13" equation, in which x-y=13; this allows you to replace (x-y) with 13, so you now have
2x=7+13.

The property allowing you to see 2x=7+13=20 is SUBSTITUTION.
You could skip the intermediary step of doing the separate substitution because knowing x-y=13 according to this given equation, either member can be understood as equal to the other. You would ordinarily just "add the two given equations", since all the coefficients on the variables are 1; and you would be able to eliminate y. ... like this:

(x+y)+(x-y)=7+13
leading directly, paying attention to how the numbers are associated on the left side, to 2x=20.
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