Solving Systems of Linear Equations: Linear Combinations

What is the solution to this system of equations? 4x + 5y = 7 3x - 2y = -12 The solution is

(-2.3,3)

The swim and diving clubs at Riverdale High School have a total of 55 members and no student is a member of both teams. of the swim team members are seniors and of the diving team members are seniors. If there are 13 seniors in the two clubs, how many members does each club have? Let x represent the total number of swim club members and let y represent the total number of diving club members. The equation that represents the total number of members isx + y = 13x+ y = 55(1/3)x + (1/5)y = 13(1/3)x+ (1/5)y = 55 . The equation that represents the total number of seniors isx + y = 13x + y = 55(1/3)x + (1/5)y = 13(1/3)x + (1/5)y = 55 . The diving club has 791325 more members than the swim club.

1) B 2)C 3)D

A deli sells sliced meat and cheese. One customer purchases 4 pounds of meat and 5 pounds of cheese for a total of $30.50. A sandwich shop owner comes in and purchases 11 pounds of meat and 14 pounds of cheese for $84.50. The system of equations below represents the situation. 4x + 5y = 30.50 11x + 14y = 84.50 The variable x represents thenumber of customersnumber of slices of meatcost per pound of meattotal pounds of meat . The variable y represents thenumber of customersnumber of slices of cheesetotal pounds of cheesecost per pound of cheese . The deli charges $3.50 for a pound of cheese2.00 for each slice of cheese4.50 for a pound of meat3.25 for each customer

1) C 2)D 3)C

Dawn has been using two bank accounts to save money for a car. The difference between account 1 and account 2 is $100. If she uses 3/8 of account 1 and 7/8 of account 2, Dawn will have a down payment of $2,000. Solve the system of equations to find the total amount of money Dawn has in each account. A - B = 100 A + B = 2,000 Dawn has $1,5701,6704,1754,275 in account 1 and $1,5701,6704,1754,275 in account 2.

1,670 1,570

Henrique began to solve a system of linear equations using the linear combination method. His work is shown below: 3(4x - 7y = 28) → 12x - 21y = 84-2(6x - 5y = 31) → -12x + 10y = -62 12x - 21y = 84+ -12x + 10y = -62 -11y = 22 y = -2 Complete the steps used to solve a system of linear equations by substituting the value of y into one of the original equations to find the value of x. What is the solution to the system?

3.5, -2

A system of linear equations is shown below, where A and B are real numbers. 3x + 4y = A Bx - 6y = 15 What values could A and B be for this system to have no solutions? A = 6, B = -4.5 A = -10, B = -4.5 A = -6, B = -3 A = 10, B = -3

A

During one month of cell phone use, Noah used 200 anytime minutes and 400 text messages, and paid $80.00. The next month, he used 150 anytime minutes and 350 text messages, and paid $67.50. Which statement is true? Each text message costs 5 cents more than each anytime minute. Each anytime minute costs 10 cents more than each text message. A text message and an anytime minute each cost 25 cents. Each text message costs double the amount of an anytime minute.

A

Alvin's first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by -3. Which linear combination of Alvin's system of equations reveals the number of solutions to the system? 9x + 4y = 36 6x + 2.5y = 24 Infinite solutions: 0x - 0y = 0 No solutions: 0x + 15.5y = 144 One solution: 0x + 0.5y = 0 Two solutions: 0x - 0.5y = 60

C

The linear combination method is applied to a system of equations: (4x + 10y = 12)(10x + 25y = 30) - 2x + 5y = 6-2x - 5y = -6 0 = 0 What does 0 = 0 indicate about the solutions of the system? There are 0 solutions to the system. The solution to the system is (0, 0). There are solutions to the system at the x- and y-intercepts. There are infinitely many solutions to the system.

D

Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? 5x + 13y = 232 12x + 7y = 218 The first equation can be multiplied by -13 and the second equation by 7 to eliminate y. The first equation can be multiplied by 7 and the second equation by 13 to eliminate y. The first equation can be multiplied by -12 and the second equation by 5 to eliminate x. The first equation can be multiplied by 5 and the second equation by 12 to eliminate x.

c