Question

Solve the system of equations: y²-x²=16, x²-y²=16 (explain and show work) Will name most brainy

Answer 1

Answer: No solutions (system is inconsistent)

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Explanation:

Rearrange the first equation into $-x^2+y^2 = 16$

So we have this equivalent system

$\begin{cases}-x^2+y^2 = 16\\\\x^2-y^2=16\end{cases}$

If you add the terms straight down, then you'll find that the x^2 and y^2 terms add to 0. The right hand side terms add to 16+16 = 32

We are left with the equation 0 = 32, which is a false equation or contradiction. Therefore, there are no solutions. We say the system is inconsistent. The two graphs do not intersect at all as shown in the diagram below. We have two hyperbolas in which the branches extend off to infinity to slowly approach the asymptotes. They never actually get to the asymptotes, but only get closer.