Multiplying One Equation to Solve Systems: Assignment

Solve this system of equations. 2x + 6y = −6, 4x − 3y = −12 What is the solution to the system of equations?

(-3, 0)

Consider the system of equations. 3x + 2y = 16, x + y = 4 Which numerical values could you multiply the second equation by to eliminate a variable? Select all that apply.

-2 -3

Which values of k would cause this system of equations to have no solution? Check all that apply. 6x + 4y = 14 3x + 2y = k

-2 5 10 21

This system of equations represents Reese's pocket change. Let n represent the number of nickels and d represent the number of dimes Reese has in his pocket. n + d = 11 5n + 10d = 70 How many dimes are in Reese's pocket?

3 dimes

Percy said that any real number for k would cause the system of equations to have no solution. Explain the error in Percy's statement. 6x + 4y = 14 3x + 2y = k

A value of k = 7 means the equations are equivalent. A system of equivalent equations has infinitely many solutions. Multiplying 2 by 3x + 2y = 7 gives the equivalent equation 6x + 4y = 14.

Which statement describes this system of equations? 9x - 6y = 15 3x - 2y = 5

The equations in the system are equivalent equations.

Reese has nickels and dimes in his pocket. He counts a total of 11 coins. The total value of his pocket change is 70 cents. Let n represent the number of nickels and let d represent the number of dimes in Reese's pocket. Which equations can be used to represent the information in this problem? Check all that apply.

n + d = 11 5n + 10d = 70

Alyssa is preparing her grocery list for the week. She wants to have a smoothie for breakfast every day and plans on a total of 6 cups of smoothies made from frozen fruit puree and yogurt. Knowing that fruit puree costs $2.00 per cup and yogurt costs $3 per cup, she budgets $14.00 for the ingredients. Which system could Alyssa's roommate Marni use to find x, the number of cups of fruit puree, and y, the number of cups of yogurt, Alyssa plans to buy?

x + y = 6 2x + 3y = 14

Consider the system of equations. 5x + 2y = 6, 10x + 4y = 12 Which equation is equivalent to the first equation of the system and can be used to solve the system using the linear combination method?5x + 2y = 1210x + 4y = 65x + 4y = 12 -10x - 4y = -12 Which answer describes the number of solutions to the system of equations?

Q1) -10x - 4y = -12 Q2) Infinite solutions

Marni writes this system to determine how much of each ingredient Alyssa plans to buy. She uses x to represent cups of frozen fruit puree and y to represent cups of yogurt. x + y = 6,2x + 3y = 14 To solve this system using the linear combination method, Marni multiplies the first equation by −2 to eliminate the x variable. −2x − 2y = −122x + 3y = 14 Finish solving the system to determine how many cups of fruit puree and yogurt Alyssa will buy. Marni determined that Alyssa plans to purchase 2345 cups of fruit puree and 2345 cups of yogurt.

Q1) 4 cups Q2) 2 cups