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MAT 1033 PRACTICE TEST #2 NAME _______________________________ INSTRUCTOR M.BEYLIN Determine whether the ordered pair is a solution of the system of linear equations. 1) (-6, -3); x + y = -9 x - y = -3 1) 2) (-5, 2); 5x = -22 - y x + 4y = 3 2) Solve the system of equations by graphing. x + 2y = 4 3) 3x - 2y = -12 3) y 10 5 -10 -5 5 10 x -5 -10 1 4) x+y=5 x-y=3 4) y 10 5 -10 -5 5 10 x -5 -10 Without graphing, decide: (a) Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point? (b) How many solutions does the system have? 5) 3x - y = 8 5) x + 4y = 20 6) y - 3x = 5 6y = 18x + 30 6) Solve the system of equations by the substitution method. 7) x + 5y = -21 -6x + 4y = -10 7) 8) 3x + y = 11 9x + 3y = 33 8) 9) -5x - 15y = 9 5x + 15y = 0 9) 2 Solve the system of equations by the addition method. 10) x + 3y = 11 -6x + 2y = -6 11) 10) 2x - 3y = 2 3x - 5y = 2 11) x y + =1 5 15 12) 13) 12) x y =0 4 12 5x - 3 y = -26 4 3x + 2 44 y=5 5 13) 3 Write a system of equations in x and y describing the situation. Do not solve the system. 14) One number is 5 more than another number. If you add 8 to 2 times the first number, the result is 3 times the second number. 14) 15) The sum of two numbers is -5. Three times the first number equals 4 times the second number. Find the two numbers. 15) 16) The three angles in a triangle always add up to 180°. If one angle in a triangle is 110° and the second is 4 times the third, what are the three angles? 16) 17) A chemist needs 70 milliliters of a 55% solution but has only 40% and 61% solutions available. Find how many milliliters of each that should be mixed to get the desired solution. 17) 18) Jimmy is a partner in an Internet-based coffee supplier. The company offers gourmet coffee beans for $12 per pound and regular coffee beans for $6 per pound. Jimmy is creating a medium-price product that will sell for $8 per pound. The first thing to go into the mixing bin was 10 pounds of the gourmet beans. How many pounds of the less expensive regular beans should be added? 18) Solve. 4 19) Dmitri needs 7 liters of a 36% solution of sulfuric acid for a research project in molecular biology. He has two supplies of sulfuric acid solution: one is an unlimited supply of the 56% solution and the other an unlimited supply of the 21% solution. How many liters of each solution should Dmitri use? 19) 20) Natasha rides her bike (at a constant speed) for 4 hours, helped by a wind of 3 miles per hour. Pedaling at the same rate, the trip back against the wind takes 10 hours. Find find the total round trip distance she traveled. 20) Determine whether the ordered pair given is a solution of the linear inequality in two variables. 21) x + 2y > -10; (3, -6) 21) 22) x ≤ y - 3; (-2, -1) 22) 5 Graph the solution of the system of linear inequalities. x ≥ 2y 23) x + 2y ≤ 6 23) y 10 5 -10 -5 5 10 x -5 -10 24) y< 1 x+8 2 y> 1 x+1 2 24) y 10 5 -10 -5 5 10 x -5 -10 6 25) x≥-1 5x + 4y ≤ -3 25) y 10 5 -10 -5 5 10 x -5 -10 Solve the problem. 26) Bruce is a retired carpenter who builds patio chairs and dog houses, which he sells at his local flea market. It takes him 3 hours to build a dog house and 4 hours to build a patio chair. Bruce can work no more than 25 hours per week, and he must produce more chairs than dog houses. Write a system of inequalities to describe this situation. Use D for the number of dog houses and P for the number of patio chairs produced in a week. 7 26) Answer Key Testname: 1033 EXAM2 REVIEW 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) Yes No (-2, 3) (4, 1) lines intersecting at a single point; one solution identical lines; infinite number of solutions (-1, -4) infinite number of solutions no solution (2, 3) (4, 2) 5 15 12) , 2 2 13) (-4, 8) 14) x - y = 5 2x - 3y = -8 20 15 15) and 7 7 16) 17) 18) 19) 20) 21) 22) 23) 110°, 56°, 14° 20 ml of 40%; 50 ml of 61% 20 lb 56% solution: 3 L; 21% solution: 4 L 80 mi Yes No y 10 5 -10 -5 5 10 x -5 -10 8 Answer Key Testname: 1033 EXAM2 REVIEW 24) y 10 5 -10 -5 5 10 x 5 10 x -5 -10 25) y 10 5 -10 -5 -5 -10 26) P>D 4P + 3D ≤ 25 9