Question

If 2x+3y=a and -x+5y=6b, express x and y in terms of a and b. (Vectors)

Answer 1

@asnaseer hi, do you know how to solve this question? :$

Answer 2

Somehow I have to use substitution? i'm not so sure.. :|

Answer 3

use the second equation to express x in terms of y and b

Answer 4

then substitute that into the first equation and rearrange to get y in terms of a and b

Answer 5

so lets start with the first step - can you rearrange the second equation to get an expression for x in terms of y and b?

Answer 6

so sorry for the late reply but is it: x=5y-6b?

Answer 7

yes, now use this to replace x in the first equation

Answer 8

so, 2(5y=6b)...

Answer 9

*-6b

Answer 10

yes, except that should be 2(5y-6b)...
use that to find an expression for y in terms of a and b

Answer 11

what do you mean?

Answer 12

ok, first substitute the expression for x into the first equation - what do you get - please write out the entire expression.

Answer 13

2(5y-6b)+3y=a

Answer 14

good - now expand the brackets

Answer 15

10y-12b+3y=a

Answer 16

great! - now gather the terms involving y and move everything else to the right-hand-side of the equals sign

Answer 17

so, 13y=a+12b?

Answer 18

yes, now divide both sides by 13 to get an expression for y in terms of a and b

Answer 19

and that's it? o.O

Answer 20

yes - that gives you y in terms of a and b.

then substitute that expression for y back into the other equation you found:

x=5y-6b

to find x in terms of a and b as well.

Answer 21

ohh, thank you! btw, how did you know that we had to use substitution (aside from telling you)? o.o

Answer 22

it was from "you telling me" :)

Answer 23

is that how the question was originally worded?

Answer 24

ohh.. what if I didn't tell you-- how would you have known? o.O

Answer 25

it would have been fairly obvious. it is just plain algebra.

Answer 26

aww man, okay thank you!

Answer 27

yw :)