# general method of solving simultaneous equ. and elimination of variable

• May 17th 2008, 03:43 AM
afeasfaerw23231233
general method of solving simultaneous equ. and elimination of variable
given $x^4+ax^3+bx^2-8x+4$ is the identity of
$x^4 +(l+c)x^3+(m+d+cl)x^2 +(cm+dl)x + dm$
then $l+c=a$
$m+d+cl=b$
$cm+dl=-8$
$dm=4$
i have to find abcdlm. i always write so many useless steps in solving simultaneous equ by elimination. would any one give me some advice and a general guide so that i could do it quick and fast without writing redundant steps? thanks.
• May 17th 2008, 03:47 AM
Moo
Hello,

Quote:

Originally Posted by afeasfaerw23231233
given $x^4+ax^3+bx^2-8x+4$ is the identity of
$x^4 +(l+c)x^3+(m+d+cl)x^2 +(cm+dl)x + dm$
then $l+c=a$
$m+d+cl=b$
$cm+dl=-8$
$dm=4$
i have to find abcdlm. i always write so many useless steps in solving simultaneous equ by elimination. would any one give me some advice and a general guide so that i could do it quick and fast without writing redundant steps? thanks.

Hmm...Is it the product abcdlm or the variables a,b,c,d,l,m that you want ?
• May 17th 2008, 07:23 AM
afeasfaerw23231233
sorry! it's just an example. that a,b,c,d,l,m cannot be found. the example doesn't work too. just want to know what is the general method to solve simultaneous equation.
• May 17th 2008, 07:28 AM
Moo
Quote:

Originally Posted by afeasfaerw23231233
sorry! it's just an example. that a,b,c,d,l,m cannot be found. the example doesn't work too. just want to know what is the general method to solve simultaneous equation.

The first thing I thought when I saw your equations was to take the equation containing the least number of variables, then substitute.

When I see an immediate factor that would eliminate a given variable, without putting too many variables into one equation, I do it..

If you have given examples, perhaps it'd help (Wink)