Systems of Equations

What is a System of Equations?

A system of equations is two or more equations that share variables with one another.
They are usually indicated by a curved bracket.

You can solve systems of equations through substituting one variable with the same variable from the other equation.
This is called the substitution method.
Alternatively you can solve them by subtracting the equations from each other, to eliminate a term to find the remaining term.
This is called the elimination method.

Systems of equations let you find variables for equations with multiple unknowns.
The amount of unknown variables there can be depends on the number of equations in the system.
If there are two equations, you can find two unknown variables, such as x and y.
If there are three equations, you can find three unknown variables, such as x, y and z.

The Gaussian method is used to solve triple systems of equations.
It uses the elimination method, and you can freely move rows around and multiply a row to cancel out values as efficiently as possible.
What you are trying to do is to cancel out the values so that you can find one of the variables, which can then easily be substituted into the other ones.
Keep in mind that you should organize the same variables to be in the same vertical columns as each other.
You should cancel out variables so that the first row has 4 terms, the second row has 3 terms and the last row has 2 terms, meaning it is a direct equation.

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