When working with Simultanious Equations Are the notations of a1 and a2 correct in this example?

Question

Is the mathematical notation of a1 and a2 correct in the following:
Can the following equation be written better to conform with Mathematical Notation?

3x + 2y = 8
3x - y = 5

3x = 8 - 2y

x = (8-2y)/3

3(8-2y)/3 - y = 5

3(8-2y) - 3y = 15

24-6y - 3y = 15

-6y - 3y = 15 - 24

-9y = -9 (a1)

y=1 (a2)

x = (8-2)/3

x = 2

Answer 1

subtracting (2) from (1)
3y=3 and so y=1
substituting
3x+2=8
3x=6 and so x=2
the soluion set={2,1}
your solution is absolutely correct

Answer 2

Correct, but hard work, try:
3x - 2y = 8 minus
3x - y = 5
gives 3y = 3
y = 1
now substitute for y in either equation
3x - 1 = 5
3x = 5 + 1
x = 2

Answer 3

you don't have to put 'a1' and 'a2'in you answer

"3x + 2y = 8
3x - y = 5

3x = 8 - 2y

x = (8-2y)/3

3(8-2y)/3 - y = 5

3(8-2y) - 3y = 15

24-6y - 3y = 15

-6y - 3y = 15 - 24

-9y = -9

y=1

x = (8-2)/3

x = 2"

your answer is correct

i hope that this helps

Answer 4

3x + 2y = 8- - - - -Equation 1
3x - y = 5 -- - - - -Equation 2
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Multiplty equation 2 by 2
2(3x) - 2(y) = 2(5)

6x - 2y = 10 New Equation 2

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Elimination by addition Method

Elimination of the y variable

3x + 2y = 8
6x - 2y = 10
- - - - - - - -
9x = 18

9x/9 = 18/9

x = 2

The answer is x = 2

Insert the x value into equatiopn 2

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Solving for y

3x - y = 5

3(2) - y = 5

6 - y = 5

6 - y - 6 = 5 - 6

- y = - 1

-1y/- 1 = -1/- 1

y = 1

The answer is y = 1

Insert the y value into equation 2

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Check for equation 2

3x - y = 5

3(2) - (1) = 5

6 - 1 = 5

5 = 5

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Check for equation 1

3x + 2y = 8

3(2) + 2(1) = 8

6 + 2 = 8

8 = 8

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The solution set { 2, 1 }

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Your answer is correct

The Elimination by addition method and the substitution method work.

Answer 5

Focusing on the use of a1 and a2 in your worked example - which is what your question is really about - I shouldn't put them there.

The a1 and a2 serve to highlight
-9y = -9 and
y = 1

-9y = -9 is the thought process immediately preceding y =1.

I see no point in highlighting the thought process, which immediately precedes one of the solutions.

There may be a virtue in highlighting the solution. If there is a virtue in highlighting one solution, there is probably a virtue in highlighting the other (x = 2).

I have never seen these a1s and a2s used before and think their use in your answer is inconsistent.

I think the basic way of expressing the answer as

y = 1
x = 2

is clear and unambiguous.

I think the smartest way (for people who understand it) is

the solution set is {2,1}

as rfamilyme expressed it.

Answer 6

However, at the line beginning
3(8-2y)/3 -

instead of multiplying through by 3, you could just divide top and bottom of this fraction by 3 and get
8 - 2y - y = 5

thus making the working slightly simpler.

Answer 7

Yes, but why not just go straight from

3(8-2y)/3 - y = 5

to

8 - 2y - y = 5

then

-3y = -3

y=1

Answer 8

Yep perfect!

Answer 9

That's perfect, your question doesn't make much sense!