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236 Chapter 3 Systems of Linear Equations and Inequalities Section 3.1 Solving Systems of Linear Equations 1. Solutions to Systems of Linear Equations A linear equation in two variables has an infinite number of solutions that form a line in a rectangular coordinate system. Two or more linear equations form a system of linear equations. For example: x 3y 5 2x 4y 10 A solution to a system of linear equations is an ordered pair that is a solution to both individual linear equations. Determining Solutions to a System of Linear Equations Example 1 Determine whether the ordered pairs are solutions to the system. 1 10, 62 2, 42 x y 6 3x y 2 a. b. Solution: a. Substitute the ordered pair into both equations: ✔ True ✔ True 12, 42 x y 6 122 142 6 3x y 2 3122 142 2 12, 42 Because the ordered pair is a solution to each equation, it is a solution to the system of equations. 10, 62 b. Substitute the ordered pair into both equations: ✔ True False x y 6 102 162 6 3x y 2 3102 162 2 10, 62 Because the ordered pair is not a solution to the second equation, it is not a solution to the system of equations. Skill Practice Determine whether the ordered pairs are solutions to the system. 1 14, 102 2, 12 1. 2. 3x 2y 8 y 2x 18 A solution to a system of two linear equations can be interpreted graphically as a point of intersection between the two lines. Concepts 1. Solutions to Systems of Linear Equations 2. Solving Systems of Linear Equations by Graphing by the Graphing Method Answers 1. No 2. Yes


miller_intermediate_algebra_4e_ch1_3
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