Topic 5: Systems

System: a group of equations simultaneously describing one situation

Solve by “Guess and Check”: Solve by first guessing a solution, then checking to see if it is valid. A wise mathematician would use the check to adjust the next guess and make it closer to a solution.

Solve by Substitution: Solve one of the equations for a variable and the substitute it into the other equation(s). Simplify the result to solve the system.

Solve by Graphing: Graph each equation and look for where all of the graphs intersect. Test those intersections as solutions.

Solve by Elimination (Linear Combinations): Rearrange the equations so that when two are added together they eliminate a variable. Simplify the result to solve the system.