Vectors
posted by annonymous
if a=3x+2y and b=5x4y, find x and y in terms of a and b
What I did:
2a=6x+4y
+b=5x4y

2a+b=x
2(3x+2y)+(5x4y)=x
6x+4y+5x4y=x
11x=x
11x dvided by x = 11
...that isn't the correct answer. The correct answer (according to text book) is
x=2/11a+1/11b
y=5/22a3/22b
I'm puzzled on how to do this with all the letters. I also don't know how to find out y. I think I did a bit of figuring for x right, right?

Reiny
you made an error in the initial addition.
2a = 6x + 4y
b = 5x  4y
add them:
2a + b = 11x
x = (2a+b)/11 or 2a/11 + b/11 , which is the given answer
now plug the x back into the first equation:
5x  4y = b
5(2a+b)/11  4y = b
times 11
5(2a + b)  44y = 11b
10a + 5b  44y = 11b
44y = 10a + 6b
y = (10a + 6b)/44
= (5a  3b)/22 , which is the same as the given y
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