# If x+2y=2 and (x+y)2=9, what is the value of y?

1. Jul 9, 2004

### Monique

Staff Emeritus
If x+2y=2 and (x+y)2=9, what is the value of y?

And the answer is not -1.. what is the trick here that I'm missing? The answer is supposed to be 5.

2. Jul 9, 2004

### NateTG

$$x+2y=2$$
so
$$x=2-2y$$
so
$$(x+y)^2=(2-2y+y)^2=(2-y)^2=9$$
square root of both sides:
$$\pm (2-y)=3$$
$$-3=2-y$$ or $$3=2-y$$
So the solutions (note the plural) are:
$$(-8,5)$$ and $$(4,-1)$$

I'm guessing you forgot that every number has two square roots. ;)

3. Jul 9, 2004

### Monique

Staff Emeritus
ahhh see? these little simple things.. thanks NateTG!

I should be doing other things at 2 in the morning :grumpy:

4. Jul 10, 2004

### fourier jr

monique is a cutie :blush: