College Algebra, 4th Edition

Chapter 5 Review and Tests

Review

Definitions, Concepts, and Formulas

Examples

5.1 Systems of Equations in Two Variables A system of equations is a set of equations with common variables. A solution of a system of equations in two variables x and y is an ordered pair of numbers $(x_1,y_1)$ that satisfies all equations in the system. The solution set of a system of two linear equations of the form $ax+by=c$ is the point(s) of intersection of the graphs of the equations. Systems with no solution are called inconsistent, and systems with at least one solution are consistent. A system of two linear equations in two variables may have one solution (independent equations), no solution (inconsistent system), or infinitely many solutions (dependent ...