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miller_intermediate_algebra_4e_ch1_3

238 Chapter 3 Systems of Linear Equations and Inequalities Solution: To graph each equation, write the equation in slope-intercept form First equation Second equation Slope: 4x 2y 6 12 2y 4x 6 2y 2 4x 2 6 2 y mx b. y 2x 3 2 Slope: y 1 2 x 2 From their slope-intercept forms, we see that the lines have different slopes, indicating that the lines must intersect at exactly one point.We can graph the lines using the slope and y-intercept to find the point of intersection (Figure 3-2). 5 4 y 1 54 3 1 2 3 4 5 21 1 2 3 4 5 Figure 3-2 x 3 2 4x 2y 6 y x 2 12 Point of intersection (2, 1) The point (2, ) appears to be the point of intersection. This can be confirmed by substituting and into both equations. 1 2 y x 2 4x 2y 6 ✔ True ✔ True The solution set is 512,126. Skill Practice Solve by using the graphing method. 3. y 3x 5 x 2y 4 6 6 1 1 8 2 6 1 1 2 4122 2112 6 1 1 2 122 2 x 2 y 1 1 TIP: In Example 2, the lines could also have been graphed by using the x- and y-intercepts or by using a table of points. However, the advantage of writing the equations in slope-intercept form is that we can compare the slope and y-intercept of each line. 1. If the slopes differ, the lines are different and nonparallel and must cross in exactly one point. 2. If the slopes are the same and the y-intercepts are different, the lines are parallel and do not intersect. 3. If the slopes are the same and the y-intercepts are the same, the two equations Avoiding Mistakes Using graph paper may help you be more accurate when graphing lines. There are many websites from which you can print graph paper. Answer represent the same line. 3. 512, 126


miller_intermediate_algebra_4e_ch1_3
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