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Math 123B Fall 2015 Instructor: Lan Ch7 Test B Name_____________________________________ Directions: Show all work in the space provided. Write answer on line or graph provided. Closed books and notes. Scientific calculator is allowed. Graphing calculators, cell phones, smart phones, laptops, iPads, tablets, etc. are not allowed.______ Determine whether the ordered pair is a solution of the system of linear equations. Show work (2 pts), Answer (2 pts) 1) (6, 3); 4pts. YES NO 4x + y = 21 3x + 4y = 6 2) (1, 4); 2x + y = 6 4x + 2y = 12 4pts. YES NO Solve the system of equations by graphing. Graphing correct lines (2 points each), Point of intersection (2 points). x - 2y = 1 6pts. Pt of intersection __________________ 3) 3x + 2y = 11 B1 Solve the system of equations by graphing. Graphing correct lines (2 points each), Point of intersection (2 points). 6pts. Pt of intersection ________________ 4) 2x + y = 3 y = -1 Solve the systems of equations by the substitution method. Show answers using ordered pairs. 5pts. 5) __________________ 5) x + y = -25 y = 4x 6) x + 3y = 17 7x + 2y = 62 5pts. 6) __________________ B2 Solve the system of equations by the substitution method. Show answer using ordered pair. 5pts. 7) __________________ 7) 5y = x - 14 7x - 6y = 11 Solve the systems of equations by the addition method. Show answers using ordered pairs. 5pts. 8) ________________ 8) x - 5y = -42 3x - 6y = -45 9) 3x - 5y = 5 2x - 3y = 5 10) -3x + 5y = 13 7x + 3y = -1 5pts. 9) __________________ 5pts. 10) __________________ B3 Solve the 3x3 systems of equation using substitution or elimination. Show answers using ordered triples. 11) x -y +z = 3 8pts. 11) __________________ x + y + z = -3 x + y - z = -7 12) 5x + 2y + z = 1 3x - 5y - z = -21 5x + y + 3z = -7 8pts. 12) __________________ B4 Questions 13 & 14. Setup, solve and show each step clearly. 3 points for setup, 3 points for work, and 2 pts. for solution. 13) Devon purchased tickets to an air show for 6 adults and 2 children. The total cost was $178. The cost of a child's ticket was $3 less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket. 8pts. A) __________________ C) __________________ 14) One number is four more than a second number. Two times the first number is 2 more than four times the second number. Find the numbers. 8pts. 14) __________________ B5 Questions 15 & 16. Setup, solve and show each step clearly. 4 points for setup, 3 points for work, and 2 pts. for solution. 15) A chemist needs 120 milliliters of a 66% solution but has only 63% and 75% solutions available. Find how many milliliters of each that should be mixed to get the desired solution. 9pts. 15) 1st____________ 2nd____________ 16) A certain aircraft can fly 720 miles with the wind in 3 hours and travel the same distance against the wind in 8 hours. What is the speed of the wind? 9pts. 16) __________________ B6 Answer Key Testname: MATH123B CH7TESTB HEMENWAY 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) No Yes (3, 1) (2, -1) (-5, -20) (8, 3) (-1, -3) (3, 9) (10, 5) (-1, 2) (-2, -3, 2) (-1, 4, -2) adult's ticket: $23; child's ticket: $20 7 and 3 90 ml of 63%; 30 ml of 75% 75 mph B7