Question

x^2-y^2=9 and y^2-2x=6 substitution method, then graph :(

Answer 1

(−3,0),(5,4),(5,−4)

Answer 2

...umm, I'll show you what I did...
first, isolate the x in the second equation so
\[y ^{2}-2x=6\rightarrow2x=y ^{2}-6 \rightarrow x=(\frac{ (y ^{2}-6) }{ 2 })\] then you plug x into the first equation so
\[(\frac{ y ^{2}-6 }{ 2 })^{2}-y ^{2}=9\] then you factor out and give it common denominators so
\[(\frac{ y ^{4}-12y ^{2}+36 }{ 4 })-y ^{2}=9 \rightarrow (\frac{ y ^{4}-12y ^{2}+36 }{ 4 })-\frac{ 4y ^{2} }{ 4 }=9\] by giving it common denominators you can now subtract so
\[(\frac{ y ^{4}-12y ^{2}+36-4y ^{2} }{ 4 })=9 \rightarrow (\frac{ y ^{4}-16y ^{2}+36 }{ 4 })=9\] then multiply by 4 on both sides and subtract 36 on both sides so
\[y ^{4}-16y ^{2}+36=9\times4 \rightarrow y ^{4}-16y ^{2}+36=36 \rightarrow y ^{4}-16y ^{2}=0\] then you can factor out a y^2 and then take the difference of squares so
\[y ^{4}-16y ^{2}=0 \rightarrow y ^{2}(y ^{2}-16)=0 \rightarrow y ^{2}(y-4)(y+4)=0\] so then you can get the values for y which are -4, 0 , and 4
then you can plug those y values into one of the (or a version of) the original equations like
\[x=(\frac{ (y ^{2}-6) }{ 2 })\]
you can probably take it from here :)
as for the graph... you can try: http://www.wolframalpha.com/input/?i=x%5E2-y%5E2%3D9+and+y%5E2-2x%3D6