Systems of linear equations

A system of linear equations consists of multiple linear equations involving the same set of variables. The solution is the set of variable values that satisfy all equations simultaneously. The most common methods to solve such systems are substitution, elimination, and graphical methods.

Important properties

• A system can have one solution (consistent and independent), no solution (inconsistent), or infinitely many solutions (dependent).

• Graphically, each equation represents a line; the solution is where the lines intersect.

• The elimination method combines equations to eliminate variables.

• The substitution method solves one equation for a variable and substitutes into the other.