This document provides an overview of solving systems of linear equations through graphing and algebra. It defines a system of equations as a set of two or more equations and describes the different types of solutions as unique (intersecting lines), inconsistent (parallel lines with no solution), or dependent (same line with infinitely many solutions). Students are given examples to solve systems of equations through both graphing and algebraic methods.

1. Finite Mathematics Mrs. Guevara

2. Warm Up Write each equation in slope intercept form

3. Objectives : Solve systems of linear equations -By Graphing and -with Algebra. Lesson 3-1A : Systems of Two Linear Equations in Two Variables.

4. System of equations : a set of two or more equations. Unique Solution : intersecting lines (only one solution). Inconsistent : parallel lines (no solution). Dependent : same line (infinitely many solutions) What is a system of Equations? What do solutions of a system look like? (x,y) Graphing Algebra x = y = 0 ≠ 2 1 ≠ 5 -4 ≠ 4 0 = 0 1 = 1 -4 = -4 x y x y x y

5. 4 2 The solution is at (4, 2). Solve the system of equations a) with Algebra & b) with Graphing.

6. The system is dependent, there are infinitely many solutions. Solve the system of equations a) with Algebra & b) with Graphing.

7. The system is inconsistent, there is no solution. Solve the system of equations a) with Algebra & b) with Graphing.

8. A26:Page 163, #30 & 31 DO NOT FOLLOW BOOK INSTRUCTIONS For each problem, solve by graphing and algebraically. 30) 31) Graph and Algebra Graph and Algebra X=? Y=? X=? Y=? (x,y) (x,y) Writing: In complete sentences, describe how the graph of a System of equations relates to the algebra when: there is one solution, no solution, or many solutions.