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5y-2-2axy-b-0-ay-2-2bx-5c-0-5x-3a-y-2-4ax-2-y-bx-5c-0-5y-2-x-5x-2a-y-ax-3-3b-0-Please-solve-simultaneously-for-x-and-y-such-that-all-four-equations-are-obeyed-




Question Number 67997 by ajfour last updated on 03/Sep/19
5y^2 +2axy+b=0  ay^2 +2bx+5c=0  (5x+3a)y^2 +(4ax^2 )y−bx−5c=0  5y^2 −x(5x+2a)y−ax^3 −3b=0  Please solve simultaneously  for x and y such that all four  equations are obeyed.
$$\mathrm{5}{y}^{\mathrm{2}} +\mathrm{2}{axy}+{b}=\mathrm{0} \\ $$$${ay}^{\mathrm{2}} +\mathrm{2}{bx}+\mathrm{5}{c}=\mathrm{0} \\ $$$$\left(\mathrm{5}{x}+\mathrm{3}{a}\right){y}^{\mathrm{2}} +\left(\mathrm{4}{ax}^{\mathrm{2}} \right){y}−{bx}−\mathrm{5}{c}=\mathrm{0} \\ $$$$\mathrm{5}{y}^{\mathrm{2}} −{x}\left(\mathrm{5}{x}+\mathrm{2}{a}\right){y}−{ax}^{\mathrm{3}} −\mathrm{3}{b}=\mathrm{0} \\ $$$${Please}\:{solve}\:{simultaneously} \\ $$$${for}\:{x}\:{and}\:{y}\:{such}\:{that}\:{all}\:{four} \\ $$$${equations}\:{are}\:{obeyed}. \\ $$

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