express the vector v as a linear combination

Question

Express the vector v=[6,2] as a linear combination of x=[-4,-1] and y=[-5,-1]

v=?x+?y

Answer 1

v=(6,2)

x=(-4,-1) and y=(-5,-1)

Let v=ax+by

so we get (6,2)=a(-4,-1) +b(-5,-1)=(-4a-5b,-a-b)

so, -4a-5b=6 and -a-b=2 clearly a=-4, b=2

=>v=-4x+2y