b) Write each equation in slope-intercept form. 4 x 8 y 10 6 x 12 y 15 8 y 4 x 10 12 y 6 x 15 y 4 8 x 10 8 y 6 12 x 15 12 y 1 2 x 5 4 y 1 2 x 5 4 The equations are the same: they have the same slope and y-intercept. Therefore, this system has an infi nite number of solutions. c) Write each equation in slope-intercept form. 9 x 6 y 13 3x 2 y 4 6 y 9 x 13 2 y 3 x 4 y 9 6 x 13 6 y 3 2 x 4 2 y 3 2 x 13 6 y 3 2 x 2 The equations have the same slope but different y-intercepts. If we graphed them, the lines would be parallel. Therefore, this system has no solution. YOU TRY 4 Without graphing, determine whether each system has no solution, one solution, or an infi nite number of solutions. a) 2x 4y 8 b) y 5 6 x 1 c) 5x 3y 12 x 2y 6 10x 12y 12 3x y 2 Using Technology In this section, we have learned that the solution of a system of equations is the point at which their graphs intersect. We can solve a system by graphing using a graphing calculator. On the calculator, we will solve the following system by graphing: x y 5 y 2x 3 Begin by entering each equation using the Y= key. Before entering the fi rst equation, we must solve for y. x y 5 y x 5 Enter x 5 in Y1 and 2x 3 in Y2, press ZOOM, and select 6: ZStandard to graph the equations. Since the lines intersect, the system has a solution. How can we fi nd that solution? Once you see from the graph that the lines intersect, press 2nd TRACE. Select 5: intersect and then press ENTER three times. The screen will move the cursor to the point of intersection and display the solution to the system of equations on the bottom of the screen. 250 CHAPTER 4 Linear Equations and Inequalities in Two Variables www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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