Question 1: Solve the equations: 3x + 2y = 12 and 3x - y = 3 by matching coefficients.

Answer: x=3, y=3

Question 2: Find the value of x and y: 5x + y = 11 and 10x - 2y = 8, using elimination by matching coefficients.

Answer: x=2, y=1

Question 3: Solve: 4x + 3y = 7 and 8x + 6y = 14. Explain whether these equations are consistent, inconsistent, or dependent.

Answer: Dependent equations; infinitely many solutions.

Question 4: Determine the values of x and y in the equations: 2x - y = 4 and 4x - 2y = ? (Complete the second equation to match the first by coefficient matching)

Answer: 8

Question 5: Solve: x + 2y = 9 and 3x + 2y = 15 by matching the coefficients of y.

Answer: x=6, y=1.5

Question 6: A problem involving real-world context: Two tanks are filled with water. Tank A has 3 liters of water and a mixture of chemicals with 2 units of chemical per liter; Tank B has 4 liters with 3 units per liter. Write equations to find when the total units of chemical are equal in both tanks, matching coefficients.

Answer: 3*2 + 3x = 4*3 + 2x

Question 7: Construct a pair of equations with matching coefficients for elimination, where the solutions for x and y are both positive integers.

Answer: e.g., 2x + 3y = 13 and 4x + 6y = 26

Question 8: Identify and correct the mistake: Students solve the system 5x + y = 10 and 5x + y = 12 by elimination, claiming the solution is x=?, y=?

Answer: They should recognize the equations are inconsistent; no solution.

Question 9: Solve for x and y: 7x - 2y = 5 and 14x - 4y = ? (Determine the second value by matching coefficients).

Answer: 10

Question 10: Challenge: Find integers x and y such that 3x + 2y = 8 and 6x + 4y = ? (Explain your reasoning).

Answer: The second equation is a multiple; equations are dependent; infinitely many solutions.

Question 11: Mixed review: Solve 2x + y = 5 and 3x + y = 7 by matching coefficients on y.

Answer: x=2, y=1