Algebra - guide no.1 page 162, 10th question

[robin_philip27]

Hi,
The question:

x+y <0
y-x>0

A B
Y 0



For me the answer seems B ( given answer D)
My steps :
x+y<0
x-y<0
-------------------
2y<0 ( Here I substrated the two inequalities
so again, by dividing both sides by 2 to get, y<0 ?

Any mistakes ?
Can you help me ?

[bultmagl]

I approach these problems using substitution trying to prove D. I would start to see if any x satisfies where y=0. It does when you substitute values x = -5, y = 0. This says y=0, or C.

Now, find an x that satisfies where y is different, maybe y=1 x = -2. It works.

So we showed D.

In your solution, you can't subtract the inequalities. When you subtract the equations, you are multiplying the entire bottom equation by (-1) and adding them. This reverses the inequality sign. So, you can't subtract inequalities with the same sign.

What you should get is x<0, y>x and y < -x. You can substitute values into these inequalities and show D.

[tommywallach]

As was stated, you can only add equations together when the inequality symbol is facing the same way:

x+y <0
0<y-x
-------
x + y < y - x
2x < 0
x < 0

So it turns out we know nothing about y's sign, hence the answer D.

-t