For rectangles with the same area, the length varies inversely as the width. One rectangle has a length of 12 cm and a
width of 5 cm. Find the length of another rectangle with the
same area whose width is 4 cm.

the correct answer to your question is a. 4^4

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not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.