Objective: Solve systems of two linear equations by substitution.
While a graph is often helpful in terms of visualizing the solution(s) to a system of equations, solving systems by graphing can be a slow process. Fortunately, there are some algebraic methods for solving systems of equations. The first of these algebraic methods, called the substitution method, involves the following steps:
1. Isolate one variable in one of the equations.
2. In the other equation, substitute the equivalent expression for that variable.
3. Solve the resulting equation to find the value of one variable.
4. 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 substitution.
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 substitution 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.