University:
Bradley University
Course:
MTH 109 | College Algebra
Academic year:

2022
Views:

416

Pages:

4
Author:

segolhandworked

Systems of Equations Test REVIEW (UNIT 6) Name Key What is the solution of the system? Use a graph. 1. y = -5x + 2 y = -2x - 1 m = -5 b = 2 m = -2 b = -1 (1,-3) 2. y = -5x + 5 y = -x + 3 m = -5 b = 5 m = -1 b = 3 Parallel lines No solution 3. y = -4x + 3 y = -3x + 5 m = -4 b = 3 m = -3 b = 5 Same line Infinite solution What is the solution of the system? Use substitution. 4. y = -x + 2 3(y - x + 1) = 2(x + 2) 3(-x + 2 + 1) = 2(x + 2) -3x + 9 = 2x + 4 -5x = -5 x = 1 y = -1 + 2 y = 1 (1,1) 6. 3x - 2y = 7 2x - y = 10 3x - 2y = 7 -2(2x - y) = -2(10) 8x - 2y = 16 -4x + 2y = -20 4x = -4 x = -1 -2(-1) - y = 10 2 - y = 10 -y = 8 y = -8 (-1,-8) 7. 2x - y = 16 8x - 2y = 28 8x - 2y = 28 -2(2x - y) = -2(16) 4x + 2y = -32 12x = -4 x = -1/3 -2(-1/3) - y = 16 2/3 - y = 16 -y = 16 - 2/3 y = -4 2/3 (-1/3, -4 2/3) 8. 3x - 5y = 6 9x + 8y = -17 9(3x - 5y) = 9(6) 7.8x + 0.1y = -39.4 27x - 45y = 54 78x + y = -394 -521x = 26053 x = -5 -5304x + 68y = -737 -5304(-5) + 68y = -737 26520 + 68y = -737 68y = -272 y = -4 (-5, -4) -70x - 41y = -175 -47x - 13y = -123 -70x - 41y = -175 -47x - 13y = -123 11. 4x + 3y = 31 -2(2x + 5y) = -2(52) 4x + 3y = 31 -4x - 10y = -104 -7y = -73 y = 5 4x + 3(5) = 31 4x + 15 = 31 4x = 16 x = 4 (4,5) 12. 4x - 2y = 2 2(2x - y) = 2(1) 4x - 2y = 2 -4x + 2y = -2 0 = 0 Infinite solutions 13. Tom has a collection of 21 CDs and Nita has a collection of 14 CDs. Tom is adding 3 CDs a month to his collection while Nita is adding 4 CDs a month to her collection. Find the number of months after which they will have the same number of CDs. Tom = 21 + 3x Nita = 14 + 4x 21 + 3x = 14 + 4x 7 = x 7 months 14. The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 46 centimeters, find the dimensions of the rectangle. P = 2l + 2w 46 = 2(3 + 3w) + 2w 46 = 6 + 6w + 2w 40 = 8w 5 = w l = 3 + 3(5) l = 18 cm 15. A corner store sells two kinds of baked goods: cakes and pies. A cake costs $10 and a pie costs $9. In one day, the store sold 15 baked goods for a total of $142. How many cakes did they sell? C = cake P = pie C + P = 15 10c + 9p = 142 -9(C + P) = -9(15) 10c + 9p = 142 -9c - 9p = -135 10c + 9p = 142 c = 7 Therefore, they sold 7 cakes.