Solving Systems by Elimination

A set of two or more equations with the same variables.

Finding the values of the variables that satisfy all equations in the system.

A technique for solving systems of equations by adding or subtracting equations to eliminate a variable.

By manipulating the equations so that when added or subtracted, one variable cancels out.

Align the equations so that corresponding variables and constants are in the same columns.

Multiply one or both equations by a number to make the coefficients equal.

A system that has at least one solution.

A system that has no solutions.

A system that has infinitely many solutions, where the equations represent the same line.

By substituting the solution back into the original equations to see if they hold true.