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messersmith_power_introductory_algebra_1e_ch4_7_10

Answer: (1, 3) Let’s graph 2x 3y 3 by plotting points. 5 y y x 4 (1, 3) 5 5 5 2x y 1 When drawing lines, be sure to extend them beyond the boundaries of your grid! Using a straightedge to graph the lines is a good idea. x y 0 1 3 3 3 1 x y 5 2x 3y 3 5 5 y x 2 5 (3, 1) 13 The point of intersection is (3, 1), so the solution is (3, 1). The solution of the system is (3, 1). The system is consistent. x Note It is important that you use a straightedge to graph the lines. If the graph is not precise, it will be difficult to correctly locate the point of intersection. Furthermore, if the solution of a system contains numbers that are not integers, it may be impossible to accurately read the point of intersection. This is one reason why solving a system by graphing is not always the best way to find the solution. But it can be a useful method, and it is one that is used to solve problems not only in mathematics, but also in areas such as business, economics, and chemistry. YOU TRY 2 Solve the system by graphing. 3x 2y 2 y 1 2 x 3 3 Solve a Linear System by Graphing: Special Cases Do two lines always intersect? No! Then if we are trying to solve a system of two linear equations by graphing and the graphs do not intersect, what does this tell us about the solution to the system? x EXAMPLE 3 In-Class Example 3 Solve the system by graphing. 3x 2 y 4 6 x 4 y 8 Answer: 5 y 3x 2y 4 5 5 5 6x 4y 8 Solve the system by graphing. 2 x y 1 2 x y 3 Solution Graph each line on the same axes. x y 5 2x y 3 5 5 2x y 1 5 The lines are parallel; they will never intersect. Therefore, there is no solution to the system. We write the solution set as . www.mhhe.com/messersmith SECTION 4.1 Solving Systems by Graphing 247


messersmith_power_introductory_algebra_1e_ch4_7_10
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