There are several methods for solving a system of 3 equations quickly, but one of the most efficient ways is by using the Gauss-Jordan elimination method. This involves converting the system of equations into an augmented matrix and using row operations to simplify and solve for the variables.
Yes, many scientific and graphing calculators have built-in features for solving systems of equations. You can input the equations and use the calculator's function to solve for the variables.
The order in which you solve the equations does not affect the final solution. However, it is often helpful to start with the simplest equation or the one that has the fewest variables, as it may make the process faster and easier.
A system of 3 equations will have a solution if the number of equations is equal to the number of variables and the equations are not parallel or coincident. This can also be determined by graphing the equations and checking for intersections.
Yes, both substitution and elimination are effective methods for solving systems of equations, but they may take longer than the Gauss-Jordan elimination method. It is recommended to use these methods if the equations are already in a simplified form.