Solving Systems of Linear Equations
Solving Systems of Linear Equations by Graphing
Graphing can be a useful strategy to determine the solution to a system of linear equations. Make sure your graphing calculator is within your reach, as you prepare to learn how to determine the solution to a system of linear equations by graphing. Click the player button to begin.
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Determining the Number of Solutions
As you learned in the interactivity above, the solution to a system of linear equations is denoted by the point where the lines of the system intersect. When a system of linear equations has one solution, the lines intersect at one point. Take a look at the graphs of the systems below to learn how to identify systems that have no solution and systems that have an infinite number of solutions.
If a system of two linear equations is represented by two parallel lines, the system has no solution. There is no point of intersection, therefore there is no solution.
If a system of two linear equations is represented by two lines that intersect at every point, the system has an infinite number of solutions. If the graph of the system appears to be the graph of a single line, the system has an infinite number of solutions.
Using the Substitution Method to Solve Systems of Linear Equations
The substitution method is another strategy that can be used to determine the solution to a system of linear equations. In this interactivity, you will learn how solving one of the equations of a system for one of its variables allows you to substitute an expression into the other equation of the system. Click the player button to begin.
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Using the Elimination Method to Solve Systems of Linear Equations
Another strategy that can be used to determine the solution to a system of linear equations is the elimination method. Before applying this method to solve a system of linear equations ensure that the equations included in the system are in standard form. Once you have mastered this strategy, you will know how to use multiplication, addition, or subtraction to eliminate a pair of variables within a system. Click the player button to begin.
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Solving Systems of Linear Equations Review
Now that you have examined how to solve systems of linear equations, review your knowledge in this interactivity. Click the player button to get started.
Did you answer the content review incorrectly? Do you want more instruction or extra practice? If so, view the videos Solving Multi-Step Linear Equations Graphically, Using the Elimination Method to Solve Systems of Linear Equations, Using the Substitution Method to Solve Systems of Linear Equations, and Using the Graphic Calculator to Solve Systems of Linear Equations from eMediaVASM.