# System of Linear Equations (Reference Card)

###### This wiki is incomplete.

A **system of linear equations** is a collection of linear equations. The equations are all to be considered at the same time. Systems of equations are used to solve problems in which there are a couple of constraints, and there are certain numerical values that satisfy those constraints.

As an example,

$\begin{aligned} x+2y & =2 \\ -x+y & =1 \end{aligned}$

is a system of equations that has two variables $x$ and $y.$ The solution to a linear system is an assignment of numbers to the variables that satisfy every equation in the system. In the example above, there is one solution: $x = 0, y=1.$ When the equations are graphed, the lines intersect at the solution.

## Writing a System of Equations

## Methods for Solving

There are several different methods for solving systems of linear equations. They are linked below.

- Substitution Method
- Elimination Method
- Graphing Method (link)
- Matrices Method (link)

**Cite as:**System of Linear Equations (Reference Card).

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/andy-test-1/