Exercise: Let $P\in {\mathbb{R}}^{V}$ be defined by the inequalities

$\begin{array}{rl}{x}_{u}\le 1& \text{for every}u\in V,\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}(1)\\ {x}_{u}+{x}_{v}\ge 1& \text{for every edge}uv\in E,\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}(2)\end{array}$

node set $V=\{1,2,3,4,5,6,7,8,9\}$

Starting from the system $(1)-(2)$, give the cutting-plane proof of the inequality

${x}_{1}+{x}_{2}+{x}_{6}\ge 2$

What I've tried: I know that I need to show that there exists a nonnegative combination from the inequalities $(1)$ and $(2)$ such that ${x}_{1}+{x}_{2}+{x}_{3}\ge 3$ holds. I don't know how unfortunately.

Question: How do I solve this exercise?

$\begin{array}{rl}{x}_{u}\le 1& \text{for every}u\in V,\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}(1)\\ {x}_{u}+{x}_{v}\ge 1& \text{for every edge}uv\in E,\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}(2)\end{array}$

node set $V=\{1,2,3,4,5,6,7,8,9\}$

Starting from the system $(1)-(2)$, give the cutting-plane proof of the inequality

${x}_{1}+{x}_{2}+{x}_{6}\ge 2$

What I've tried: I know that I need to show that there exists a nonnegative combination from the inequalities $(1)$ and $(2)$ such that ${x}_{1}+{x}_{2}+{x}_{3}\ge 3$ holds. I don't know how unfortunately.

Question: How do I solve this exercise?