<s>[INST] Finding average of two variables in two equation The given equations are:
$$7x+3y=17$$
and
$$3x+7y=19$$
How can i find the average of two variables $x$ and $y$ with simple calculation steps?
 [/INST] Since we got two (differing from each other) formulas with only 2 unknown numbers, we can quite easily calculate both $x$ and $y$. I'll explain my steps, without using matrices, just algebra (just like you asked).
So, we got $7x + 3y = 17$ and $3x + 7y = 19$. Because we can say $17 = 19 - 2$ we can state that 
$$7x + 3y = 3x + 7y - 2$$
We take away $3x$ and $3y$ on both sides and we get
$$4x = 4y - 2$$
We divide both sides by $4$ and we get
$$x = y - \frac{1}{2}$$
Now, if we use that in our first equation, it becomes
$$7(y - \frac{1}{2}) + 3y = 17$$
$$7y - 3\frac{1}{2} + 3y = 17$$
We add $ 3\frac{1}{2}$ on both sides and it says
$$10y = 20\frac{1}{2}$$
Now we divide both sides by 10, and we calculated $y$!
$$y = 2\frac{1}{20}$$
And since we already know that $x = y - \frac{1}{2}$ we calculated that 
$$x = y - \frac{1}{2} = 2\frac{1}{20} - \frac{10}{20} = 1\frac{11}{20}$$
Now, if you still want the average, it is 
$$\frac{x + y}{2} = \frac{2\frac{1}{20} + 1\frac{11}{20}}{2} = \frac{72}{40} = 1\frac{32}{40} = 1\frac{4}{5}$$
There you go
EDT: Whoops, looks like I made a mistake somewhere since the answer is not correct, but you get the idea.
EDT2: Corrected the mistake (typo) thanks to the comments :) and this is in accordance with the answer placed by the question asker himself, so that's entirely correct!
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