Objective: Solve systems of two linear equations by elimination.
The second algebraic method for solving a system of equations, called the elimination method, involves the following steps:
1. Rewrite both equations in the form Ax + By = C.
2. If necessary, multiply one or both equations by a constant so that terms containing the same variable have opposite coefficients.
3. Add the two equations to eliminate one variable.
4. Solve the resulting equation to find the value of one variable.
5. Substitute this value into one of the equations to find the value of the other variable.
Watch the video below to see examples of how to solve systems of two linear equations by elimination.
Remember that when solving a system of two linear equations, there are three possible outcomes: one solution (intersecting lines), no solutions (parallel lines) and infinite solutions (same line for both equations). When solving a system by an algebraic method, if the result is an equation that is always false, such as 5 = 6, the system has no solution. If the result is an equation that is always true, such as 5 = 5, the system has infinite solutions. Examples of solving these types of systems by elimination are shown in the video below.
Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the next lesson.