Solve by elimination.
[tex](\vec A + 3\, \vec B) - (\vec A - \vec B) = (-3\,\vec\imath + \vec\jmath) - (\vec\imath - 2\,\vec\jmath)[/tex]
[tex]\implies 4\,\vec B = -4\,\vec\imath + 3\,\vec\jmath \implies \boxed{\vec B = -\vec\imath + \dfrac34\,\vec\jmath}[/tex]
[tex]\implies \vec A = \vec\imath - 2\,\vec\jmath + \vec B[/tex]
[tex]\implies \boxed{\vec A = -\dfrac54 \,\vec\jmath}[/tex]
