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System of equations

# Introduction to systems of equations

A system of equations is a collection of two or more equations that contains the same variables.

This is a system of two equations with two variables:

$\left{3x+y=4\\2x-3y=-1$

In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.

x=1, y=1 are solutions of the system $\left{3x+y=4\\2x-3y=-1$

Let's see: 3·1+1=4 and 2·1-3·1=-1.
They satisfy both equations in the system.

There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.