Vectors

Remember that    a(x1, y1)   - b(x2, y2 ) =   ( ax1 - bx2, ay1  - by2 )

a(3,4)  - b(2,4)   =  (8,10)

So we have that

3a  - 2b  = 8      and

4a  - 4b  = 10

Multiply the first equation by - 2  all the way through

-6a  + 4b  =  -16     

4a  -   4b   =  10        add these

-2a   =  -6     divide both sides by  -2

a  = 3

And using   3a  - 2b  = 8  to  find b, we have that

3(3)  - 2b  = 8

9  - 2b  = 8 

-2b  = -1

b  = 1/2

b = 1/2