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Mentallic

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I have had quite a bit of experience solving simultaneous equations from highschool (haven't learnt matrices) by various - but mostly - rearranging one variable and substituting it into another equation, but recently I was attempting to remove a surd upon another surd (lack of a better word) and came up with quite a toughy ~

[tex]a^2+2b^2+3c^2+6d^2=4[/tex]

[TEX]2ab+6cd=1[/TEX]

[TEX]ab+2bd=0[/TEX]

[TEX]2ad+2bd=1[/TEX]

I know from experience that attempting to solve simultaneous equations that are more difficult than 3 linear equations in 3 variables will just lead to a big mess and lead me down the path of major frustration and book throwing escapades.

What would be the best approach for such a problem? Should I start chugging at it and just hope I have the solutions before I forget why I even attempted this in the first place?

Thanks for any advice.

[tex]a^2+2b^2+3c^2+6d^2=4[/tex]

[TEX]2ab+6cd=1[/TEX]

[TEX]ab+2bd=0[/TEX]

[TEX]2ad+2bd=1[/TEX]

I know from experience that attempting to solve simultaneous equations that are more difficult than 3 linear equations in 3 variables will just lead to a big mess and lead me down the path of major frustration and book throwing escapades.

What would be the best approach for such a problem? Should I start chugging at it and just hope I have the solutions before I forget why I even attempted this in the first place?

Thanks for any advice.

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