Two cars leave town going in opposite directions. One car is traveling 65 miles per hour (mph), and the other car is traveling 50 mph. How long will it take before the cars are 575 miles apart?

[6.05] Which set of equations would be used to solve this word problem? An airplane flew 5 hours with a 50 mph head wind. The return trip with a tail wind of the same speed took 3 hours. Find the speed of the plane in still air. d = 5(r − 50) and d = 3(r + 50) ◄ Ans Question 2 (Multiple Choice Worth 5 points) [6.05] Which equation would you use to solve the following word problem? Sasha's mom decided to get her a cell phone for her birthday. Cell Plus has a plan that costs $23.95 per month plus an additional $0.05 per minute. Cell Best has a plan that costs $28.95 per month plus an additional $0.03 per minute. How many minutes can Sasha talk and have the same cost each month? 23.95 + 0.05m = 28.95 + 0.03m ◄ Ans Question 3 (Multiple Choice Worth 4 points) [6.01] The graph of a system of parallel lines has no solutions. Always ◄ Ans Question 4 (Multiple Choice Worth 5 points) [6.03] Solve the following system. x − y = 10 ← eq1 x + y = 6 ← eq2 eq1 + eq2 2x = 16 x =8 multiply eq1 with (-) & eq1 + eq2 2y = -4 y = -2 ===================== x = 8 & y = -2 (8, -2) ◄ Ans ====================== Question 5 (Multiple Choice Worth 4 points) [6.02] Henri solved the system of equations below. What mistake did he make in his work? 3x + y = 6 ← eq1 x − 2y = 2 ← eq2 y = 6 − 3x x − 2(6 − 3x) = 2 x − 12 + 6x = 2 7x − 12 = 2 x = 2 3(2) + y = 6 6 + y = 6 y = 0 He made no mistake. ◄ ans Question 6 (Multiple Choice Worth 5 points) [6.05] There were 170 people at the Junior-Senior dance Sasha and her friends attended. Junior tickets were $2.00 each and Senior tickets were $3.50 each. The total receipts for the dance were $490. How many Juniors bought tickets? Let J = Junior attended : S = Senior attended J + S = 170 ← eq1 $2J + $3.5 S = $490 2J + 3.5S = 490 2(170 - S) + 3.5S = 490 340 - 2S + 3.5S = 490 340 + 1.5S = 490 1.5S = 490 - 340 S = 150/1.5 S = 100 J + S = 170 J = 170 - 100 J = 70 ◄ Ans Question 7 (Multiple Choice Worth 4 points) [6.03] If you wanted to eliminate the y variable in the following system, what could be your first step? x − y = 6 −4x − 4y = 10 Multiply the first equation by −4. ◄ Ans Question 8 (Multiple Choice Worth 4 points) [6.02] For the following system, if you isolated x in the first equation to use the Substitution Method, what expression would you substitute into the second equation? x − y = 8 −x − y = −7 8 + y ◄• Ans Question 9 (Multiple Choice Worth 4 points) [6.03] What is the value of the x variable in the solution to the following system of equations? 3x + 2y = 6 ← eq1 2x + 3y = −1 ← eq2 eq1 x3 → 9x + 6y = 18 eq2 x-2→ -4x - 6y = +2 Add 4x = 20 x = 4 4 ◄• Ans Question 10 (Multiple Choice Worth 5 points) [6.05] Two cars leave town going in opposite directions. One car is traveling 65 miles per hour (mph), and the other car is traveling 50 mph. How long will it take before the cars are 575 miles apart? 65(T) + 50(T) = 575 5 hrs ◄• ans Question 11 (Multiple Choice Worth 4 points) [6.01] The graph of the following system of equations is −2x + y = 3 −4x + 2y = 6 Parallel lines ◄• Ans [6.06] The graph below is represented by which system of inequalities? graph of two inequalities. One inequality is dashed, and goes through the points (1, 0) and (0, 3), and is shaded in above the line. The other inequality is dashed, and goes through the points (5, 0) Question 13 (Multiple Choice Worth 5 points) [6.01] Select the system of equations that corresponds to the given graph. graph of two lines. Both lines go through the points negative 1 comma 2 and 2 comma 0 ======================= 2x + 3y = 8 −x + y = −4 ◄• Ans ======================= Question 14 (Multiple Choice Worth 5 points) [6.06] Which point lies in the solution set for the following system of inequalities? 2x + y > 8 x − y < 2 (3, 4) ◄• Ans Question 15 (Multiple Choice Worth 4 points) [6.02] Solve the following system. y = x + 3 2x + y = 9 - y = -x - 3 ← multiply by (-1) y = - 2x + 9 0 = -3x + 6 x = 2 y = x + 3 y = 2 + 3 y = 5 (2, 5) ◄• Ans Question 16 (Multiple Choice Worth 4 points) [6.02] Washington High School has a total of 90 boys and girls who play sports. If the number of boys is 10 more than three times the number of girls, how many girls play sports at this high school? Let B = boys G = girls B+G = 90 ←eq1 B = 10 + 3G ← eq2 eq1 in eq2 10 + 3G + G = 90 4G = 80 G = 20 20 ◄ • ans

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