Question

Solve the following pair of equations for the vectors u and v.
Assume i = <1,0> and j = <0,1>.
8u +7v = i , u - v = j

u = ( )i + ( )j
v = ( )i + ( )j

Can someone explain to me how to solve this?

Answer 1

setup the equations ...
let u = (xu, yu) and v=(xv,yv)

8u = (8xu, 8yu) and 7v=(7xv,7yv)
1u = (xu, yu) and -1v = (-xv, -yv)

then its just a matter of adding the parts and addressing the system of equations that resutls

Answer 2

8u = (8xu, 8yu)
+7v = (7xv,7yv)
----------------
1 , 0


1u = ( xu, yu)
-1v = (-xv, -yv)
---------------
0 , 1

Answer 3

Forgive me, but I'm not following...