SOLUTION: ax+by=u cx+d y=v when d is=[a b c d]=/0 what is the answer

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Question 251662: ax+by=u
cx+d y=v when d is=[a b c d]=/0 what is the answer
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
I think I understand your question. Let's first solve for x and y in terms of a, b, c, d, u, and v.
multiply the first equation by c and the second equation by -a:
c%28ax+%2B+by+=+u%29
-a%28cx+%2B+dy+=+v%29
This will eliminate the x variable and we can solve for y.
cby+-+ady+=+cu+-+av
So, y equals
(i) +y+=+%28cu+-+av%29+%2F+%28bc+-+ad%29
substituting that into the first equation for x, we get
ax+%2B+b%28cu+-+av%29%2F%28bc-ad%29+=+u
Solving for x, we get
(ii) X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-ad%29%29%29%2Fa
Now we have solve for X and Y in terms of a, b, c, d, u, and v.
-----
Case 1: let d = a.
From (i and ii) we get
X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-a%5E2%29%29%29%2Fa
+y+=+%28cu+-+av%29+%2F+%28bc+-+a%5E2%29
-----
case 2: let d = b.
From (i and ii) we get
X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-ab%29%29%29%2Fa - -> X+=+%28u+-+%28%28cu+-+av%29%2F%28c-a%29%29%29%2Fa
+y+=+%28cu+-+av%29+%2F+%28bc+-+ab%29
-----
case 3: d = c.
From (i and ii) we get
X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-ac%29%29%29%2Fa
+y+=+%28cu+-+av%29+%2F+%28bc+-+ac%29
-----
case 4: d = d
From (i and ii) we get
X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-ad%29%29%29%2Fa
+y+=+%28cu+-+av%29+%2F+%28bc+-+ad%29
I hope that helps and is what you were looking for.