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## Homework Statement

Consider a feasible region S defined by a set of linear constraints

S = {x:Ax<b}

Prove that S is convex

## Homework Equations

All what i know is that, a set is convex if and only if the elements x, and y of S

ax + (1-a)y belongs to S

for all 0 <a < 1

## The Attempt at a Solution

I don't even know where to begin!