There is no way to get either x or y without getting rid of one somehow. You can't just throw the number away, it must be set as something equal. That's subbing.
Either solve for a variable, plug it in the other equation, and find the value of that variable, or add or subtract the equations from each other. There is no other way to work the problem (besides variations and maps... ex: graph)
Solve for Var:
x + y = 3 --> y = 3 - x
2x + y = 5 = 2x + (3 - x) = x + 3 = 5 --> x = 2
x + y = 3 = 2 + y --> y = 1
Subtract:
x + y - (2x + y) = 3 - 5 = -2 = -x --> x = 2
x + y = 3 = 2 + y --> y = 1
Simple as 3.14159
*sigh* I hate puns...
D3V said:
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A friend of mine has his own little way where you use ratios and shit.
He has got it to work with many a weird thing like your:
x+y=3
2x+y=5
We've been taught to rearrange it, the method is what you'd probably call subbing.
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I'll ask him how he does the ratio thing.
Or someone could have fun with a few ratios, and work backwards from the answer of x=2, y=1, which Shinto kindly gave at the start of the equation, meaning we didn't have to work it out.
Even if there is another way, solving simulateous equations is the best, and most importantly easiest way to do so. Why create more work for yourself when the solution is already at a trivial way to solve?
The general motivation is to find new ways to do a bulk of things... Perhaps to revolutionize something... If, however, the method's you're discovering have been well known and established for hundreds of years, you should look elsewhere.
D3V said:
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well, my friend has said, if cant be done any other way. And i would LOVE to prove him wrong. And who knows, maybe if by finding another way will solve something else.
It can be done by matrices, let me go dig up my algebra notebook because I seem to have forgotten how..
Ah nevermind I remembered:
Code:
So x+y=3 and 2x+y=5. Matrix is
[1 1 3]
[2 1 5] now mR1(-2)+R2 (multiply row 1 by -2 {the inverse of 2} and add the results to row 2) You end up with:
[1 1 3]
[0 -1 -1] now mR2(1) + R1, you get:
[1 0 2]
[0 -1 -1] now mR2(-1) to get:
[1 0 2]
[0 1 1]
Row 1: x=2
Row 2: y=1
Done.
This is just one of the matrix methods I learned. A couple are easier, one is a bitch load harder. Also, you can do this on your calculator in 3 seconds.
That doesn't have a damn thing to do with matricies.
You simply organized the numbers into columns and rows, and did the exact same thing I did before, which was add or subtract the equations.
Well to be fair I didn't read what you did
And it is a matrix because it's in standard matrix gaussian form (or whatever the fuck it's called). There are other methods that involve adding and subtracting matrices also that work, but they're more annoying to do.
Linear Mode
