Question 1: Match the coefficients in the equations below to eliminate x: (1) 3x + 4y = 12 (2) 6x + 5y = 20 Identify the coefficients to multiply each equation by so that the x terms cancel out.

Answer: Multiply (1) by 2 and (2) by -1

Question 2: Calculate the value of y when the equations are solved after matching coefficients: 3x + 4y = 12 6x + 5y = 20

Answer: 4

Question 3: Identify the error: A student tries to eliminate y by multiplying the first equation by 5 and the second by -4, but ends up with incorrect results. What mistake did they make?

Answer: They did not multiply all terms properly, possibly missing coefficients or signs.

Question 4: Solve the system below using matching coefficients: 2x + 3y = 8 4x + y = 10 Show your working.

Answer: x=2, y=2

Question 5: In the following system, identify whether matching coefficients can be used directly: 5x + 2y = 7 3x + 4y = 9 Explain your reasoning.

Answer: Yes, multiply equations to match coefficients of either variable, e.g., for x: 15 and 9, or for y: 8 and 12.

Question 6: Construct a pair of equations where matching coefficients will eliminate y but not x.

Answer: Possible example: 2x + 3y = 7 and 4x + 3y = 10

Question 7: A student claims that multiplying the first equation by 3 and the second by 2 will always allow elimination of x. Is this true? Why or why not?

Answer: Not always; the coefficients of x in the original equations must be multiples for elimination to work directly.

Question 8: Solve the system: 7x - 2y = 11 3x + 4y = 5 Use matching coefficients method. Show all steps.

Answer: x=2, y=-1

Question 9: Identify the common misconception in this solution: 'To eliminate y, I multiplied the first equation by 4 and the second by -3, but I didn't get the same coefficient for y.' What went wrong?

Answer: They did not multiply all terms properly, or they did not get the same y-coefficient.

Question 10: Find the solution to the system where the coefficients are mismatched initially, then correct the approach: 2x + y = 4 3x + 2y = 5

Answer: x=1, y=2

Question 11: Challenge: Create a system of equations where matching coefficients is not possible without manipulating the equations further. Explain why.

Answer: Coefficients are not multiples of each other, so direct matching is impossible without additional steps.