3.1.1 Using Graphs and Tables to Solve Linear Systems
Key Objectives • Verify solutions of linear systems. • Solve linear systems by using graphs and tables. • Classify systems of equations and determine the number of solutions. • Write and solve systems of equations. Key Terms • A linear system is a system of equations containing only linear equations.
• A system of equations is a set of two or more equations that contain two or more variables. • An independent system of linear equations is a system of linear equations with different slopes resulting in exactly one solution. • A dependent system of linear equations is a system of linear equations with equal slopes and equal y -intercepts that has infinitely many solutions. • A consistent system is a system of equations or inequalities that has at least one solution. • An inconsistent system is a system of equations or inequalities that has no solution. Example 1 Verifying Solutions of Linear Systems The solution of a system of equations must satisfy each equation in the system. So any point that is a solution to a system of equations will have x - and y -coordinates that satisfy all equations in the system.
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