One solution : There is one set of variables that would make all the equations in the system true. If they are linear equations, these lines would run parallel to each other. On a graph, the lines representing the equations do not touch. No solution : There are no variables that would make all the equations in the system true. There are three possible solution types for systems of linear equations: Repeat as necessary, such as when there are more than two linear equations in the system. Plug the resulting variable into either of the original equations and solve:Ĥ. Plug the resulting variable into the other equation and solve:ģ. Solve for or in one of the equations by isolating the variable:Ģ. Main steps for solving a system of linear equations by substitution:ġ.
The variables that satisfy both equations are and orĦ. Plug this variable into one of the original equations and simplify to isolate the remaining variable: Solve the equation to isolate the remaining variable:ĥ. Add or subtract the equations to eliminate their common variable:Ĥ. Multiply one or both of the equations by non-zero numbers that would make one set of terms cancel each other out if added or subtracted:ģ. Rewrite the equations so the variables are in the same order:Ģ. Main steps for solving a system of linear equations by elimination:ġ. These are called systems of linear equations and we can find their variable(s) using one of two methods: elimination and substitution. Sometimes we are given two or more equations that can be made true by the same variable or variables. If you have access to a graphing calculator, try graphing each equation and comparing the results.
Though these equations may all look different, they all actually represent the same line. Important: In this form, and cannot both be zero ( ). It usually has constants and variables, which cannot contain exponents or roots, and is usually written in one of the following ways: A linear equation is an equation that represents a straight line.
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