Question 1: Solve for x and y: 3x + 2y = 12 and 6x + 4y = ?

Answer: 12

Question 2: Match the coefficients to eliminate y: 5x + 3y = 10 and ?

Answer: 10x + 15y = 30

Question 3: Solve the system: 4x - y = 7 and 8x - 2y = ?

Answer: 14

Question 4: Construct an equation similar to 2x + 3y = 8 that, when matched with 4x + 6y = ?, eliminates y.

Answer: 16

Question 5: Using elimination, solve: 7x + 2y = 14 and 14x + 4y = ?

Answer: 28

Question 6: A real-world scenario: A shop sells pencils and pens. The total cost of 3 pencils and 2 pens is £5, and 6 pencils and 4 pens is £10. Write the equations and solve for the cost of each item using matching coefficients.

Answer: Pencils = £0.50, Pens = £1

Question 7: Determine the value of k so that the equations 3x + ky = 6 and 6x + 2ky = ? can be solved by elimination.

Answer: 12

Question 8: Solve the system: 2x + 5y = 9 and 4x + ky = 14, where k=10. Use matching coefficients.

Answer: x=1, y=1

Question 9: Identify and correct the mistake: Students try to eliminate y by multiplying the first equation by 3 and the second by 2, but they forget to match the coefficients correctly. Explain the mistake and provide the correct setup.

Answer: Incorrect coefficients lead to no elimination; proper matching requires equal coefficients for y, e.g., 3*(ax + by) and 2*(cx + dy).

Question 10: Challenge: Find the values of a and b so that the system 2ax + 3by = 5 and 4ax + 6by = ? can be solved by elimination, but the second equation is a multiple of the first.

Answer: Any a, b where second equation is 2 times the first; e.g., a=1, b=1