# Math Help - Simultaneous equations

1. ## Simultaneous equations

x+y=7, x^2 - y^2 = 21
How do I do this?

2. Originally Posted by Detanon
x+7=7, xsquared - ysquared = 21
How do I do this?
Did you make a typo? I ask because I only see one equation with y in.

As is stands $x =0$ and $y = \pm i\sqrt{21}$

3. Do you not "see" that x=0 ?

4. woops sorry, I fixed it now.

5. Originally Posted by Detanon
woops sorry, I fixed it now.
As that's better

You can use the difference of two squares on the quadratic

$(x+y)(x-y) = 7(x-y) = 21 \: \:$

$\therefore \: \: x-y = 3 \: \: \rightarrow \: \: x = 3+y$

Sub in x=3+y into the first equation

(3+y)+y=7

Solve that for y then use the first equation (in either form) to find x

6. I dont get how you get (x+y)(x-y).

7. Originally Posted by Detanon
I dont get how you get (x+y)(x-y).
It is the difference of two squares.
Difference of two squares - Wikipedia, the free encyclopedia

From the difference of two squares we see that $x^2-y^2=(x+y)(x-y)$

If you expand the right hand side using FOIL the LHS is obtained: $(x+y)(x-y) = x^2-xy+xy-y^2$

Since $-xy+xy=0$ we get $(x+y)(x-y)=x^2-y^2$

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EDIT: If you prefer you can use the substitution method

$x = 7-y$

$(7-y)^2-y^2=21$

and solve that linear equation (y^2 cancels) but I think using the difference of two squares is easier