Question

How do you solve the system of linear equations: `(a+2b)x+(2a-b)y=2` and `(a-2b)x+(2a+b)y=3`?

Answer 1

`x=1/(2a)-1/(5b)` and `y=1/a+1/(10b)`

Explanation:

We have `(a+2b)x+(2a-b)y=2` ...................(1)

`(a-2b)x+(2a+b)y=3` ...................(2)

Adding the two we get `2ax+4ay=5` ...................(3)

and subtracting (2) from (1), we get

`4bx-2by=-1` ...................(4)

Multiplying (3) by `2b` and (4) by `a`, we get

`4abx+8aby=10b` ...................(5)

and `4abx-2aby=-a` ...................(6)

Subtracting (6) from (5), we have

`10aby=10b+a` or `y=(10b+a)/(10ab)=1/a+1/(10b)`

Multipying (6) by `4` and adding to (5), we get

`20abx=10b-4a` or `x=(10b-4a)/(20ab)=1/(2a)-1/(5b)`