Elementary  Row Operations
used in system of equation to solve for solutions
1. Interchange two rows (or columns).
2. Multiply each element in a row (or column) by a non-zero number.
3. Multiply a row (or column) by a non-zero number and add the result to another row (or column).

EcHELON Form
form of system of equation in which the a variable in the first is not included in the second up to the last and the variables of the first variable in each equation is one.
 to get echelon arrange the variables first and use elementary  row operatiions to get the echelon form..


ex.of echelon form
x+3y+4z=22
      y+3z=12
           z=3

after that use back subtitution to find the solutions.. substitute the value of the variable on the third equation in the echelon form and substitute the corresponding values to the first to find the variable leading in the first equation.
so z=3 then y+3(3)= 12 then y= 3 then substitute to the first x+3(3)+4(3)=22 then x= 1
so the solution is in this form (x,y,z) then (1,3,3) is the solution..

other way to solve system of equations