1. System of Linear Equations Solutions 2023 (RVHS)

River Valley High School, Mathematics Department 2023 Systems of Linear Equations T1 Solutions Systems of Linear Equations 1 Let y = ax3 + bx2 + cx + d, where a, b, c and d are real constants. When x = 0, y = 0,  d = 0 Given x = 2, y = 0, a(23) + b(22) + c(2) = 0 8a + 4b + 2c = 0 ------ (1) Given x = 2.55, y = – 0.0631, a(2.553) + b(2.552) + c(2.55) = – 0.0631 ------ (2) Differentiating y with respect to x, 2d 32d y ax bx cx    Given x = 0.785, d 0d y x  , 3(0.7852)a + 2(0.785)b + c = 0 ------ (3) Solving (1), (2) and (3) using GC, a = 0.0993, b = – 0.497, c = 0.596 (3 s.f.) Hence, y = 0.1x3 – 0.5x2 + 0.6x. 2 Let $x, $y and $z be the cost of a ticket for a senior citizen, adult and child respectively. 2 19 9 1982 10 3 908 7 4 778 x y z yz x y z        Using GC, 36 74 56 x y z    Thus, the cost of a ticket for a senior citizen is $36, for an adult is $74 and for a child is $56. 4(36) + 5(74) + 1(56) = 570 Therefore, the total cost for Group D = $570

River Valley High School, Mathematics Department 2023 Systems of Linear Equations T2 3 420 6.4 17.5 25 100 102.4 420 3.8 18.5 19 120 92.6 420 8.6 17 23 90 121.2 a b c a b c abc                or 17.5 25 100 324 (1) 18.5 19 120 331.2 (2) 17 23 90 307.4 (3) a b c a b c abc             Using GC, 58 13 14,,5 5 25a b c   4 Let S, B and W be the number of strawberry, blueberry and walnut muffins purchased respectively. 30 1.6 1.75 2.2 53.40 2 2 0 S B W S B W S W S W           From GC, 12, 12, 6S B W   5 Let x, y, z be the price rate of electricity, gas and water respectively. 23 12 16 103 33 16 21 142 49 22 33 209 x y z xyz x y z        Solving 2.2x , 2.5y , 1.4z Her monthly utility bill for the month of July is        35 2.2 1.07 17 2.5 0.95 2 159.1656 1. 14 159. 7   6 Let the number of diagonals be 2d An Bn C   No of diagonals in a triangle = 0 No of diagonals in a quadrilateral = 2 Triangle (3 sides) Quadrilateral (4 sides) Pentagon (5 sides)

River Valley High School, Mathematics Department 2023 Systems of Linear Equations T3 No of diagonals in a pentagon = 5 Therefore, 9 3 0 16 4 2 25 5 5 A B C A B C A B C          Solving using GC, 13, , 022A B C   Thus, 213 22d n n For a polygon of 200 sides, The number of diagonals = 213(200) (200) 1970022  7(i) m : weight of mackerel in kg s : weight of salmon in kg t : weight of tuna in kg 800 7 21 39 20300 5 23 49 23900 m s t m s t m s t          Using GC, 200, 250, 350.m s t   Therefore the fisherman has 250 kg of salmon. (ii) m : weight of mackerel in kg s : weight of salmon in kg t : weight of tuna in kg 600 7 21 39 20