Express the variable from the equation

When solving systems of linear equations with many variables, there is often a need to express a particular variable from the equation.

How it is done? Let's take equation 2x+10y+3z=10. It contains three variables X, Y, Z. Using the online calculator, depending on the need for expressing a particular variable, the equation 2x+10y+3z=10 transforms:
- through z into an equation of the form z = (-2x-10y+10)/(+3);
- through y into an equation of the form y = (-2x-3z+10)/(+10);
- through x into an equation of the form x= (-10y-3z+10)/(+2).

The obtained value of the variable X, Y or Z can be substituted into the next equation of the system. As a result, there will be one less unknown variable in it. Expressing a variable from equations is required when solving linear programming tasks aimed at determining the values of efficiency indicators of the (objective function) in various directions.

Solving systems of linear equations is required for determining important indicators of complex practical production and other tasks:
- equipment loading,
- production planning,
- composing the feed ration for fattening animals,
- use of raw materials, etc.