Solving Systems of Linear Equations

Solving Systems of Linear Equations

• WWF Developer

  You can find the answer in pretty much any book that explains matrix math.

  With only two equations, look up “determinants”.

  For more than two, look up Gaussian decomposition.

  For a zillion equations, it gets a little more specialized…

  
  
  

• Avi_harush

  How to program something like this Easy enough:

  First of all make the user enter the equation in a normalized form, e.g. for a equation with 3 variables:

  a*x + b*y + c*z = d
  e*x + f*y + g*z = h
  i*x + j*y + k*z = l

  where the user is asked for inputs a to l.

  Then systematically eliminate variables:
  take the first equation and eliminate "x" in all other equations, e.g. for the second equation by dividing all factors of equation 1 by a and multiplying them with e and substracting equation 1 from 2. Do that for the second equation and y afterwards and so forth... once you got the last variable value figured out, insert bottom up into the equations to get the rest.

  Of course pay attention to entries of 0 for the user input and so forth, but that is an easy method of programming something like this... have fun...

  
  

• manukahn

  
  
  Anyone
  
  
  

• DrFlick

  Hi Avotas,

  are you looking how to solve linear equations in general, or just for the specific case you mentioned If it is just a specific case as above with the values always being 190 and 169 then:

  190 = (F/2) + A

  169 = ((F/2) - A) * -1

  Then replacing 190 = X and 169 = Y:

  A = (X + Y) / 2

  Substituting back into equation 1 you get F = X - Y. So if you want to turn this into code it would be:

  int x = 190;

  int y = 169;

  double a = (x + y) / 2;

  double f = x - y;

  Mark.

  
  
  
• Solving Systems of Linear Equations