Substitute in the first and the last equation:
Substract the first from the second:
Substitute v2:
Now solve the quadratic.
Find two perpendicular vectors such that one of these vectors is twice as long as the other, and their sum is the vector [6,8]. I tried the following approach.
Let's say that u = [u1,u2] and v=[v1,v2].
Then we would have the u1v1 = -u2v2. I also got the following equations.
u1+v1=6
u2+v2=8
2v1^2 + 2v2^2 = u1^2 + u2^2. I'm having trouble combining the equation to get an equation with only one variable.