Solve Linear Systems Algebraically Part I Chapter 3.2

Solutions of Linear Systems of Equations A linear system of equations will always have one of the following as a solution Exactly one solution in x and y (the lines intersect in a single point) An infinite number of solutions (the lines coincide and share all points) No solution (the lines are parallel and never intersect) The next slide shows how graphs of the last two would look

Solutions of Linear Systems of Equations

Solve Linear Systems Algebraically Although it is possible to solve a linear system of equations by graphing, this is seldom the best method The reason is that, if the solution is not an ordered pair with integer coordinates, then the point of intersection has fractional values These are usually impossible to read unless the coordinate plane is broken in the right fractional values The best method for solving a linear system of equations is by algebraic methods

Solve Linear Systems Algebraically You will learn about two such methods The first is called the substitution method The second is called the elimination method (or sometimes it is called the addition method) In today’s lesson you will solve linear systems by the substitution method This method is best used when one or both equations are solved for either y or for x

The Substitution Method

A System With No Solution

A System With Infinite Solutions

Guided Practice

Exercise 3.2a Handout