#1**+3 **

We can make \(x^2 - y^2 = -12\) into \((x-y)(x+y) = -12\) by using “Difference of Squares”. Since we know that \(x+y = 6\), we can substitute that in. Now we have \(6(x-y) = -12\). We can divide \(6\) on both sides, which gives us \(x - y = -2\). We also still have the equation \(x + y = 6\). We can use elimination to get rid of \(x\). We will subtract the second equation from the first. This gives us \(-2y = -8\), so \(y = 4\). We can plug this back into any equation to get \(x\). So \(y = 4\) and \(x = 2\).

- Daisy

dierdurst
Aug 25, 2018

#2**+2 **

Thanks, Daisy !!!.....Just wanted to try this one , too....I like these kinds of problems ....

x^2 - y^2 = -12 and x + y = 6 (1)

(x + y) ( x - y) = -12

6 ( x - y) = -12

x - y = -2 (2)

Add (1) and (2) and we have that 2x = 4 ⇒ x = 2

And y = 2 + y = 6 ⇒ y = 4

So (x ,y) = ( 2, 4)

CPhill
Aug 25, 2018