2 Equations, 2 Unknowns

Introduction

Consider the below system of equations:

2x - y = 0
-x + 2y = 3

This can be envisioned in three ways.

The equations can be plotted together, and all intersections of the lines are solutions to the system.

The system is equivalent to the following linear combination of columns.

 ┌  ┐    ┌  ┐   ┌  ┐
 │ 2│    │-1│   │ 0│
x│-1│ + y│ 2│ = │ 3│
 └  ┘    └  ┘   └  ┘

Column 1 is represented as a vector to (2,-1); column 2 as (-1,2). Any combination of these vectors that leads to (0,3) is a solution to the system.