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55) The graph shows the percentage of foreign students in U.S. institutions of higher learning from Saudi Arabia and the United Kingdom from 2004 to 2008. (http://nces.ed.gov) Percentage of Foreign Students 1.6 1.4 1.2 1.0 0.8 0.6 0.4 Saudi Arabia United Kingdom 2004 2005 2006 2007 2008 Year Percentage a) When was there a greater percentage of students from the United Kingdom? 2004–2006 b) Write the point of intersection of the graphs as an ordered pair in the form (year, percentage) and explain its meaning. c) During which years did the percentage of students from the United Kingdom remain the same? 2004–2006 d) During which years did the percentage of students from Saudi Arabia increase the most? How can this be related to the slope of this line segment? 2006–2007; this line segment has the most positive slope. 56) The graph shows the approximate number of veterans living in Connecticut and Nevada from 2006 to 2010. (www.census.gov) Number of Veterans Nevada Connecticut 254,000 250,000 246,000 242,000 238,000 234,000 230,000 2006 2007 2008 2009 Year 2010 Number 41) x y A. (0, 3.8) B. (4.1, 0) C. (2.1, 0) D. (0, 5) B; (4.1, 0) is the only point on the positive x-axis. 42) x y A. (4, 0) B. a1 3 , 0b C. (0, 3) D. (0, 2) D; (0, 2) is the only point on the positive y-axis. Objective 4: Determine the Number of Solutions of a System Without Graphing 43) How do you determine, without graphing, that a system of equations has exactly one solution? The slopes are different. 44) How do you determine, without graphing, that a system of equations has no solution? The slopes are the same, but the y-intercepts are different. Without graphing, determine whether each system has no solution, one solution, or an infi nite number of solutions. 45) y 5x 4 46) y 2 3 x 9 y 3x 7 y 2 3 x 1 one solution 47) y 3 8 x 1 48) y 1 4 x 3 no solution 6x 16y 9 2x 8y 24 49) 15x 9y 27 50) 7x y 6 10x 6y 18 x y 13 51) 3x 12y 9 52) 6x 4y 10 x 4y 3 21x 14y 35 53) x 5 54) y x x 1 no solution y 2 one solution no solution infi nite number of solutions infi nite number of solutions one solution one solution infi nite number of solutions www.mhhe.com/messersmith SECTION 4.1 Solving Systems by Graphing 253


messersmith_power_introductory_algebra_1e_ch4_7_10
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