What is the solution of the following system?
{3x-3y=10
-9x-9y=-30

Question

What is the solution of the following system?
 {3x-3y=10   
  -9x-9y=-30

paounn · Answer

multiply 1st equation by 3 and sum to the second, you get $$-18y = 0 \rightarrow y=0$$ by substituting thatresult in any of the equation (easier in the first one) you get $$3x -3*0 = 10 \rightarrow 3x = 10 x= 10/3$$.
solution is then $$x={10\over 3}; y=0$$

hero · Answer

@Burningitdown double-check for sign errors

anonymous · Answer

Uhm. @Hero  I think there may have been one, yeah.

anonymous · Answer

@Paounn  Thanks. I made a mistake in typing the problem, but I appreciate your effort.

anonymous · Answer

It should have been, 
{3x+3y=10   
  -9x-9y=-30

hero · Answer

Now that we have corrected the mistakes, 

Divide both sides of the second equation by -3 to get
3x + 3y = 10

Then realize that both equations are the same. Thus infinite solutions

paounn · Answer

Now that it's fixed ( :D ) you can see that second equation is obtained from the first by multiplying by -3 b oth terms: they are, in fact, the *same* equation. System admits $$\infty^1$$ solutions, given by $$x = t, y= {{10-3t} \over 3} t \mathbb{R}$$

anonymous · Answer

You both basically said the same thing, so I'll fan you both. Thanks.

anonymous · Answer

I greatly appreciate it.

hero · Answer

But without me, you wouldn't have found your mistake.