Solving Systems Equations

Graphing, Elimination, and Substitution

Types of Solutions

When you are finding the solution for two linear equations, you are finding their point of intersection. The point of intersection is called a solution. When solving you could find one solution, no solution, or many solutions as depicted below.
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1. Solving by Graphing

When solving by graphing, you graph both lines in order to find their point of intersection.
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2. Substitution

1. Solve one equation for one of the variables.

2. Substitute the resulting expression into other equation to replace the variable.

3. Substitute to solve for the other variable.


(Remember that you can check all of these by plugging in both values to see if they satisfy the equation.)

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3. Elimination

1. Multiply both or one equation by a number to result in two equations that have opposite terms.

2. Add the equations, eliminating one variable. Then solve.

3. Substitute to solve for the other variable.

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