Questions on Algebra: Evaluation of expressions, parentheses answered by real tutors!

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Question 152619: 1 The sum of two numbers is 12. One number is 5 times the other. Can you write the algebraic expressions for these two equations? Can you tell me what the two numbers are?
I know it is 10 and 2 but need all algebraic expressions
2. We know that if you multiply two negative numbers together you always get a positive number. We know that if you perform an arithmetic operation on rational numbers you always get a rational number as the answer. Are there any such rules for irrational numbers? Give examples.
: 1 The sum of two numbers is 12. One number is 5 times the other. Can you write the algebraic expressions for these two equations? Can you tell me what the two numbers are?
I know it is 10 and 2 but need all algebraic expressions
2. We know that if you multiply two negative numbers together you always get a positive number. We know that if you perform an arithmetic operation on rational numbers you always get a rational number as the answer. Are there any such rules for irrational numbers? Give examples.

Answer by Fombitz(1755) (Show Source):
You can put this solution on YOUR website!
First number is x.,
Second number is y.
1.
2.
You can then substitute eq. 2 into eq. 1.
1.

Then from 2,
2.

.
.
.
The rules for irrational numbers are similar.
Adding or subtracting two irrational numbers gives an irrational number.
Multiplying or dividing irrational numbers can give either rational or irrational numbers.
.
.
.
Examples:
Irrational number
Rational number
.
.
.
Irrational number
Rational number