Answer
$y=3v_1+v_2+v_3$, or $[5\ 7]=3[1\ 1]+[-1\ 2]+[3\ 2]$, is an affine combination of the vectors.
Work Step by Step
In this problem, we want to present $y=[5\ 7]$ as a linear combination of the basis vectors $v_1=[1\ 1]$, $v_2=[-1\ 2]$, and $v_3=[3\ 2]$, if possible. Through a trial and error process in which we think about how best to use $v_2$ as a counterbalance against the positive first position values of the other vectors, we find $y=3v_1+v_2+v_3$.
