Question 1)(adsbygoogle = window.adsbygoogle || []).push({});

{(u1,u2) : -∞ < (u1+u2)/2 < ∞ and -∞ < (u1-u2)/2 < ∞ } = {(u1,y2) : -∞ < u1 < ∞ and -∞ < u2 < ∞}

Why is the equality(=) true? How can I see that the two sets describe the same region?

Question 2)

2) Define u1=y1+y2, u2=y1-y2, so the mapping (or function) is (u1,u2)=f(y1,y2)=(y1+y2,y1-y2). If -∞ < y1 < ∞ and -∞ < y2 < ∞ are the DOMAIN of this mapping, then this implies the RANGE is -∞ < u1 < ∞ and -∞ < u2 < ∞. WHY?

Can someone explain, please? Any help would be appreciated!

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# Solving inequalities in TWO variables?

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