University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2019
Views:

451

Pages:

2
Author:

Adriel Kelley

Day 6 After Core Name [Name is illegible] ID: 1 Practice: Solving Systems of Equations (3 Different Methods) Date [Date is blank] Solve each system by substitution. 4x + 3y = -8 -8x + y = -12 y = 8x - 12 4x + 3(8x - 12) = -8 4x + 24x - 36 = -8 28x - 36 = -8 28x = 28 x = 1 y = 8(1) - 12 y = 8 - 12 y = -4 (1, -4) 4x - 2y = 8 y = -2 4x - 2(-2) = 8 4x + 4 = 8 4x = 4 x = 1 (1, -2) 14x - 2y = 46 7x + y = -23 y = 7x - 23 14x - 2(7x - 23) = 46 14x - 14x + 46 = 46 46 = 46 IMS (Infinitely Many Solutions) 5x + y = 8 y = -5x + 8 -3x + 2y = -10 -3x + 2(-5x + 8) = -10 -3x - 10x + 16 = -10 -13x + 16 = -10 -13x = -26 x = 2 y = -5(2) + 8 y = -10 + 8 y = -2 (2, -2) Solve each system by elimination. 10x - 8y = 4 2(-5x + 3y = -9) 10x - 8y = 4 -10x + 6y = -18 -2y = -14 y = 7 10x - 8(7) = 4 10x - 56 = 4 10x = 60 x = 6 (6, 7) -15x + 9y = 27 9(-5x - y = 17) -15x + 9y = 27 -45x - 9y = 153 -60x = 180 x = -3 -15(-3) + 9y = 27 45 + 9y = 27 9y = -18 y = -2 (-3, -2) -7x - 8y = -23 2(4x + 4y = 12) -7x - 8y = -23 8x + 8y = 24 x = 1 -7(1) - 8y = -23 -7 - 8y = -23 -8y = -16 y = 2 (1, 2) -3x - 10y = -4 3(x - 5y = 18) -3x - 10y = -4 3x - 15y = 54 -25y = 50 y = -2 -3x - 10(-2) = -4 -3x + 20 = -4 -3x = -24 x = 8 (8, -2) Solve each system by graphing. y = (5/7)x + 4 y = (-1/7)x - 2 [Graph with lines and intersection point marked] (-7, -1) x = 7 y = -x + 9 [Graph with lines and intersection point marked] (7, 2)] PICK 11. or 12 The senior classes at High School A and High School B planned separate trips to the state fair. The senior class at High School A rented and filled 10 vans and 6 buses with 276 students. High School B rented and filled 5 vans and 2 buses with 117 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry? students 15 vans 21 buses students to x = vans y = buses 10x + 6y = 276 -2(5x + 2y = 117) 10x + 6y = 276 -10x - 4y = -234 2y = 42 y = 21 10x + 6(21) = 276 10x + 126 = 276 10x = 150 x = 15 New York City is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 1 van and 6 buses with 324 students. High School B rented and filled 9 vans and 3 buses with 264 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry? x = van y = bus x + 6y = 324 -> x = 324 - 6y 9x + 3y = 264 9(324 - 6y) + 3y = 264 2916 - 54y + 3y = 264 -51y = -2652 y = 52 x + 6(52) = 324 x + 312 = 324 x = 12 12 on a van 52 on a bus A boat traveled 280 miles downstream and back. The trip downstream took 7 hours. The trip back took 14 hours. Find the speed of the boat in still water and the speed of the current. SKIP A boat traveled 252 miles downstream and back. The trip downstream took 12 hours. The trip back took 84 hours. What is the speed of the boat in still water? What is the speed of the current? SKIP