Systems of equations can be solved using elimination, substitution and matrix method. Worksheets are provided for systems of equations with two and three variables. Equations with two variables represent straight lines whereas three variables represent planes. This page focuses on solving equations and not to explain the behavior based on solutions.
Solving Equations with Two Variables
System of equations with two variables represent two staight lines. Solving equations help to find the point of intersection of lines. If the lines are parallel, then there are no point of intersection and we have no solution. If the lines lie one over the another, then there are infinitely many solutions.Otherwise, we have point of intersection and unique solution. Problems provided in Elimination method can also be solved using substitution method.
Elimination is the standard method to solve any system of equations. By making coefficients of like variable same, we can eliminate those variables that helps to find out value of another variable.
Equations in three variables represent planes. There are three types of solutions unique, infinite and no solution. Elimination method is not as easy as in two variables. No special worksheets for elimination method is provided. But you can use the same worksheets for elimination method provided in "substitution" or "any method" column.
Substitution method of solving equations with three varibles are usually harder than in two variables.