Solving Linear Systems by Graphing: A Comprehensive Guide
This guide explains how to solve a system of two linear equations using graphing techniques. A solution is defined as an ordered pair (x, y) that satisfies both equations. When graphing the equations, the goal is to identify the point of intersection, which represents the solution to the system. Key steps include converting equations to slope-intercept form, graphing them accurately, estimating the intersection coordinates, and confirming the solution algebraically by substituting back into the original equations. Learn these essential skills for effective linear equation solving!
Solving Linear Systems by Graphing: A Comprehensive Guide
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Presentation Transcript
Section 7.1 Solving Linear Systems by Graphing
A System is two linear equations: • Ax + By = C • Dx + Ey = F • A Solution of a system of linear equations in two variables is and ordered pair (x, y) that ___________ each equation in the system. • When graphing both equations for the linear system, you are looking for the ___________ of the linear equations. Where A, B, C, and D are integers and x & y are variables satisfy Solution
Checking the intersection point • Use the graph to solve the system of linear equations. Then check your solution algebraically.
Rules for Solving a linear system using graphing and check • Write each equation in slope intercept form (y=mx + b) • Graph both equations thoroughly (neatness counts) • Estimate the coordinates of the point of intersection • Check the coordinates algebraically by substituting into each equation of the original linear system.
