Linear Combination of vectors

We want to find $\lambda$ and $\mu$ so that $\vec{w}=\lambda\vec{u}+\mu\vec{v}$. We have: $$(-5,2)=\lambda(-1,2)+\mu(1,2)=(-\lambda,2\lambda)+(\mu,2\mu)= (-\lambda+\mu,2\lambda+2\mu)$$ De manera que: $$\left. \begin{array}{r} -\lambda+\mu=-5 \\ 2\lambda+2\mu=2 \end{array} \right\} \Rightarrow \lambda=3, \ \mu=-2$$ We have just found values for $\lambda$ and $\mu$ for which $\vec{w}=\lambda\vec{u}+\mu\vec{v}$. Therefore, we can express $\vec{w}=(-5,2)$ as a linear combination of $\vec{u}=(-1,2)$ and $\vec{v}=(1,2)$.