Math Example: Solving Linear Systems by Using Matrices: Example 01

Topic

Systems of Equations

Description

This example solves the system x + y = 5 and x - y = 1 using augmented matrices. The matrix is row-reduced to reveal the solution x = 3 and y = 2. This system demonstrates the method for solving a linear system by the two equations. The variables x and y represent solutions that satisfy both equations simultaneously.

Systems of equations are foundational in algebra, offering tools to find points of intersection of lines or solutions to real-world problems involving multiple constraints. These examples provide diverse methods to approach and solve such systems, enriching student comprehension.

Multiple worked-out examples are crucial in teaching mathematical concepts. They allow students to see varied approaches, understand subtleties, and gain confidence in applying methods to new problems. Consistent exposure to different examples reinforces learning and encourages adaptability.

Teacher Script: Let us analyze this example. Notice how the two equations, This example solves the system x + y = 5 and x - y = 1 using augmented matrices. The matrix is row-reduced to reveal the solution x = 3 and y = 2, are solved to find values for x and y. Pay attention to the method used and how each step is justified to ensure accuracy.

For a complete collection of math examples related to Linear Systems click on this link: Math Examples: Linear Systems Collection.