Question 1: Solve for x and y: 2x + 3y = 12 and 4x - y = 10. Use matching coefficients.

Answer: x=3, y=2

Question 2: Find the values of x and y: 5x + 2y = 20 and 10x + 4y = ?

Answer: 40

Question 3: Match the coefficients to eliminate y: 3x + 4y = 16 and 6x + ky = 24. What is the value of k?

Answer: k=8

Question 4: Construct the system of equations with matching coefficients for x and y such that the solution is x=2, y=3.

Answer: Possible equations: 4x + 5y = 23 and 8x + 10y = 46.

Question 5: Solve: 7x - 2y = 5 and 14x - 4y = ?

Answer: 10

Question 6: In solving equations 3x + ky = 9 and 6x + 2y = 12, what value of k allows elimination of y?

Answer: k=2

Question 7: Find the solution for the system: x + 4y = 9 and 2x + 8y = ?

Answer: 18

Question 8: A problem involves two quantities: 3a + 2b = 12 and 6a + 4b = ?. Find the value of the second expression.

Answer: 24

Question 9: Identify and correct the mistake: Solve 2x + 3y = 7 and 4x + 6y = 16. What's wrong with matching coefficients here?

Answer: The second equations are multiples, but the constants do not match, so no unique solution exists.

Question 10: Challenge: Find x and y such that 4x + 5y = 20 and 8x + 10y = 40, then verify the solution.

Answer: Any x, y satisfying 4x + 5y = 20; solutions are infinite

Question 11: Explain why matching coefficients might fail when the equations are dependent, using an example.

Answer: Because the equations are multiples of each other, leading to infinitely many solutions or no solution.