Linear Combinations

Given vectors ${\mathbf{v}}_1,{\mathbf{v}}_2,...,{\mathbf{v}}_{\mathbf{p}}\in {\mathbb{R}}^n$, and scalars $c_1,c_2,...,c_p,$ the vector $\mathbf{y}$ where $\mathbf{y}=c_1{\mathbf{v}}_1+c_2{\mathbf{v}}_2+...+c_p{\mathbf{v}}_{\mathbf{p}}$ is called a linear combination of ${\mathbf{v}}_1,{\mathbf{v}}_2,...,{\mathbf{v}}_{\mathbf{p}}$ with the weights $c_1,c_2,...,c_p.$ This is also called a vector equation.

We need $c_1\text{ and }{c}_2$ such that: $c_1\left[\begin{array}{c}1\\ 1\end{array}\right]+c_2\left[\begin{array}{c}-1\\ 1\end{array}\right]=\left[\begin{array}{c}1\\ 3\end{array}\right]$

So, $\left[\begin{array}{c}{c}_1\\ c_1\end{array}\right]+\left[\begin{array}{c}-c_2\\ c_2\end{array}\right]=\left[\begin{array}{c}1\\ 3\end{array}\right]$ So finally,

$$c_1-c_2=1$$ $$c_1+c_2=3$$

Same question, can $\mathbf{y}$ be represented as a linear combination of ${\mathbf{v}}_1\text{ and }{\mathbf{v}}_2$:

Thus, the system is inconsistent (no consistent).