Ch. 5 - Systems of Equations and Inequalities
Back
- In Exercises 1–5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.
Problem 1
- In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (2, 3) x + 3y = 11 x - 5y = - 13
Problem 1
- In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (- 3, 5) 9x + 7y = 8 8x - 9y = - 69
Problem 2
- In Exercises 1–5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.
Problem 2
- In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (2, 5) 2x + 3y = 17 x + 4y = 16
Problem 3
- In Exercises 5–18, solve each system by the substitution method. x + y = 4 y = 3x
Problem 5
- A chemist needs to mix a solution that is 34% silver nitrate with one that is 4% silver nitrate to obtain 100 milliliters of a mixture that is 7% silver nitrate. How many milliliters of each of the solutions must be used?
Problem 7
- In Exercises 5–18, solve each system by the substitution method. x + 3y = 8 y = 2x - 9
Problem 7
- The perimeter of a table tennis top is 28 feet. The difference between 4 times the length and 3 times the width is 21 feet. Find the dimensions.
Problem 9
- In Exercises 5–18, solve each system by the substitution method. x = 4y - 2 x = 6y + 8
Problem 9
- In Exercises 5–18, solve each system by the substitution method. 5x + 2y = 0 x - 3y = 0
Problem 11
- In Exercises 5–18, solve each system by the substitution method. 2x + 5y = - 4 3x - y = 11
Problem 13
- In Exercises 5–18, solve each system by the substitution method. 2x - 3y = 8 - 2x 3x + 4y = x + 3y + 14
Problem 15
- In Exercises 5–18, solve each system by the substitution method. y = (1/3)x + 2/3 y = (5/7)x - 2
Problem 17
- In Exercises 19–30, solve each system by the addition method. x + y = 1 x - y = 3
Problem 19
- In Exercises 19–30, solve each system by the addition method. 2x + 3y = 6 2x - 3y = 6
Problem 21
- In Exercises 19–30, solve each system by the addition method. x + 2y = 2 - 4x + 3y = 25
Problem 23
- In Exercises 19–30, solve each system by the addition method. 4x + 3y = 15 2x - 5y = 1
Problem 25
- In Exercises 19–30, solve each system by the addition method. 3x - 4y = 11 2x + 3y = - 4
Problem 27
- In Exercises 19–30, solve each system by the addition method. 3x = 4y + 1 3y = 1 - 4x
Problem 29
- In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x = 9-2y x + 2y = 13
Problem 31
- In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. y = 3x - 5 21x - 35 = 7y
Problem 33
- In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 3x - 2y = − 5 4x + y = 8
Problem 35
- In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x + 3y = 2 3x + 9y = 6
Problem 37
- In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x/4 - y/4 = −1 x + 4y = -9
Problem 39
- In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 2x = 3y + 4 4x = 3 - 5y
Problem 41
- In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is 7. If one number is subtracted from the other, their difference is -1. Find the numbers.
Problem 43
- In Exercises 47–48, solve each system by the method of your choice. (x + 2)/2 - (y + 4)/3 = 3 (x + y)/5 = (x - y)/2 - 5/2
Problem 47
- In Exercises 47–48, solve each system by the method of your choice. (x - y)/3 = (x + y)/2 - 1/2 (x + 2)/2 - 4 = (y + 4)/3
Problem 48
- In Exercises 49–50, solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0, b ≠ 0 5ax + 4y = 17 ax + 7y = 22
Problem 49
