[tex]\vec{u} = i+j$ $ ;\quad \vec{v} = i-j \\ \\ \vec{a} = x\cdot \vec{u} +y\cdot\vec{v} = x\cdot (i+j)+ y\cdot (i-j) = x\cdot i+x\cdot j+y\cdot i-y\cdot j = \\ =i\cdot (x+y) + j \cdot(x-y) \Rightarrow \vec{a} = (x+y)i+(x-y)j \\ \\ \vec{a} = 5i-j \Rightarrow \Big\{x+y = 5 \quad $si$ \quad x-y = -1 \Big\} $(le adunam)\Rightarrow \\ \\ \Rightarrow 2x = 5-1 \Rightarrow \boxed{x = 2} \\ \\ 2-y = -1 \Rightarrow \boxed{y = 3}[/tex]
