Vectors Homework Help pleasee!

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menal

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I have an assignment due on sunday and I have been stuck on 2 questions for the past 3 days! so please if anyone can answer them:

how would i do this question?
3x-2y=a and 5x-3y=b express vectors x and y terms of a and b

and: explain why the vectors a=(-2,3) b=(3,-1) = (13, -9)
 
menal said:
express vectors x and y terms of a and b
Click to expand...

As soon as you do this part, the second should be apparent. Give it a go.
 
Oh, I got that question...i got:
x=2/21a-2/7b
y=-1/7a-3/7b

*I think i did something wrong on x=2/21a <--the denominator has to be seven right?

I just need help with the second part.
 
No, the first part yet remains. Better try that again. How did you get that?
 
1. 3x-2y=a
2. 5x-3y=b

i chose number one and solved for x. and i got x=(a+2y)/3
i then subsituted x into number two and got (5a-35y)/15 and solved for y and got y=-1/7a-3/7b
and i then plugged in y back into number one
3x-2(-1/7a-3/7b) and solved for x
and i got x=2/21a-2/7b

what did i do wrong? because i have a similar question in my txtbook and i did it the same way and got the correct answer that was on the back of the book.
 
\(\displaystyle x = \frac{a+2\cdot y}{3}\)

That's fine, but I can't tell where you went, after that.

\(\displaystyle 5\left[\frac{a+2\cdot y}{3}\right] - 3\cdot y = b\)

\(\displaystyle \frac{5\cdot a+10\cdot y}{3} - 3\cdot y = b\)

\(\displaystyle 5\cdot a+10\cdot y - 9\cdot y = 3\cdot b\)

\(\displaystyle y = 3\cdot b - 5\cdot a\)

I'm not seeing any "35"s in there? How did you get one of those? Not to mention that 15 in the denominator. Something very funny going on in there.
 
OHH i expanded out the five and multiplied it by the 3 to get 15 and thn i found a common denominator of 15...

but i see where i went wrong. I plugged in what you gave me for y an got 2b+10/3a as x
is it correct now?
 
When was your last algebra class? It seems some brushing up may be in order.

x = 2b - 3a
y = 3b - 5a

It's way easier than you keep concluding.
 
thank you so much!

can you help me with the second question too?
 
Not really. It's not clear what is wanted. We can find separate expressions for x and y, but to have it magically reduce to a single vector? No.

Let's see if we can get ALL the problem statement. Then we can tack a hack at it.
 
this is exactly what it says on my sheet:

explain why the vectors a=(-2,3) and b=(3,-1) = (13,-9)

i tried using the x2-x1,y2-y1 formula, but that did not work. i have no idea what to do next
 
I got nothin'. Sorry. Small wonder you don't know what to do next. When you determine what is wanted, let us know.
 
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