Editing System of linear equations (section)

===Elimination of variables===
The simplest method for solving a system of linear equations is to repeatedly eliminate variables. This method can be described as follows:
# In the first equation, solve for one of the variables in terms of the others.
# Substitute this expression into the remaining equations. This yields a system of equations with one fewer equation and unknown.
# Repeat steps 1 and 2 until the system is reduced to a single linear equation.
# Solve this equation, and then back-substitute until the entire solution is found.

For example, consider the following system:
: <math>\begin{cases}
x+3y-2z=5\\
3x+5y+6z=7\\
2x+4y+3z=8
\end{cases}</math>
Solving the first equation for ''x'' gives <math>x=5+2z-3y</math>, and plugging this into the second and third equation yields
: <math>\begin{cases}
y=3z+2\\
y=\tfrac{7}{2}z+1 
\end{cases}</math>
Since the LHS of both of these equations equal ''y'', equating the RHS of the equations. We now have: 
: <math>\begin{align}
3z+2=\tfrac{7}{2}z+1\\ \Rightarrow z=2
\end{align}</math>
Substituting ''z'' = 2 into the second or third equation gives ''y'' = 8, and the values of ''y'' and ''z'' into the first equation yields ''x'' = −15. Therefore, the solution set is the ordered triple <math>(x,y,z)=(-15,8,2) </math>.