Matrices aren't necessary. Also, guess and check is still easier. Here's to algebra:
Basically, you have 4 variables and several equations, namely:
3x=a
8x=2b
2y=2a+b
We only need to find the "smallest" set of a,b,x, and y, which makes this question possible. Otherwise, we would need 4 equations.
Using the first two equations, we can form a relation between a and b:
24x=8a
24x=6b
0=8a-6b
8a=6b
4a=3b
The smallest integer solution is a=3 and b=4. That means x=1. Now we solve for y.
2y=2a+b
2y=6+4
2y=10
y=5.
In conclusion, a=3, b=4, x=1, and y=5. Note this is possible only because we took the smallest integer solution for 4a=3b. Otherwise, at best, we would have the coefficients in terms of one variable.
Thanks to Joe Shmo for pointing out an error.
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01 Nov '07 01:58>
Originally posted by twilight2007 Matrices aren't necessary. Also, guess and check is still easier. Here's to algebra:
Basically, you have 4 variables and several equations, namely:
3x=a
8x=4b
2y=2a+b
We only need to find the "smallest" set of a,b,x, and y, which makes this question possible. Otherwise, we would need 4 equations.
Using the first two equations, we can form a ...[text shortened]... tion for 2a=3b. Otherwise, at best, we would have the coefficients in terms of one variable.
First I thank you for showing me, I had an inkling of an idea, but not enough education.
only the answers you provided don't balance the equation.
On your second equation down If I have got the logic correct you have
8x=4b and believe it should be 8x=2b
could that be where your mistake is, I would check it myself but I'm not sure how exactly to solve this yet.
What Twilight2007 does can be done a bit faster using matrices. The method used by him/her is by far the most enlightening method 🙂
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02 Nov '07 12:09>
Originally posted by TheMaster37 What Twilight2007 does can be done a bit faster using matrices. The method used by him/her is by far the most enlightening method 🙂
Whats cool about it, is that i can actually reproduce the results.....thanks in no small part to those here at RHP
I just had a hunch, but boy is it sweet when they turn out to be correct 😀