Math Example--Systems of Equations--Solving Linear Systems by Graphing: Example 8

Topic

Systems of Equations

Description

This example solves the system of equations using graphing: The equations y = -4x + 1 and y = 4x + 4 are graphed to find the intersection at (-0.375, 2.5). The graph highlights where the two lines meet. Systems of equations involve finding the point of intersection of two or more equations. The graphical method visually demonstrates the solution by plotting the equations on the coordinate plane.

The topic of systems of equations is fundamental in algebra and helps students understand how multiple relationships can coexist and interact. By analyzing points of intersection, students gain a deeper understanding of simultaneous solutions. Examples like this provide a clear visual representation of how to identify solutions in a graph.

Seeing multiple worked-out examples is critical for students to fully grasp a concept. Each example highlights unique aspects of the problem-solving process, reinforcing understanding and helping students recognize patterns. These examples offer scaffolding to support deeper learning and independent problem-solving skills.

Teacher Script: Let's explore this system of equations. Notice how each line represents an equation. Where the lines intersect is the solution to the system. How can we confirm this solution is correct? Let's substitute the coordinates of the intersection back into both equations to verify they are true.

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