Solving Systems of Linear Equations: Linear Combinations Answers

Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together?5x + 13y = 23212x + 7y = 218

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 = 22y = –2

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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.

number of customersnumber of slices of cheesetotal pounds of cheese✔ cost per pound of cheese

3.50 for a pound of cheese2.00 for each slice of cheese✔ 4.50 for a pound of meat3.25 for each customer

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.

x + y = 13x + y = 55✔ (1/3)x + (1/5)y = 13(1/3)x + (1/5)y = 55

7913✔ 25

✔ (–2, 3)(3, –1)(7, 3)(13, –9)

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.

✔ 1,5701,6704,1754,275