SOLUTION: Solve: ax + by = m and cx + dy = n Determine x and y. Not sure how to solve. Non - homework.

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Question 1127148: Solve:
ax + by = m and cx + dy = n
Determine x and y.
Not sure how to solve. Non - homework.
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


I'll try to get you pointed in the right direction and assume that you know some algebra and can finish the problem on your own.

You can find an expression for x by eliminating y from the two equations. To do that, multiply each equation by an appropriate constant so that the coefficients of the y terms in the two equations are the same. Then subtracting one equation from the other will eliminate y, giving you an equation you can solve for x.
   ax + by = m
   cx + dy = n


** This line modified in response to reader's question **
Multiply the first equation by d and the second by b; then subtracting the second equation from the first eliminates y, allowing you to solve for x:

   adx + bdy = dm
   bcx + bdy = bn
  ---------------
   (ad-bc)x  = dm-bn

   x = (dm-bn)/(ad-bc)

You COULD plug that expression for x into one of the original equations to find the expression for y; but that would be ugly. It's easier to use the same procedure as above for solving for y.
   ax + by = m
   cx + dy = n

Multiply the first equation by c and the second by a to make the coefficients of x the same.  Then, similar to above, subtract one equation from the other to eliminate x, allowing you to solve for y.
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!

--

preparing for elimination method, to be able to eliminate y:




, actually eliminate y and find x:




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