Question 1: Solve for x and y: x + y = 7 and y = x² - 2.

Answer: x=3, y=4

Question 2: Find the solutions to the system: 2x - y = 1 and y = x² + 3.

Answer: x=2, y=7

Question 3: Calculate the values of x and y that satisfy: x + 2y = 10 and y = x²/4.

Answer: x=4, y=3

Question 4: Plot the graph of y=2x on the grid provided.

Answer: Student draws a straight line passing through coordinates (0,0), (1,2), (2,4), etc.

Question 5: Construct a parabola on the grid that passes through points (0,0), (2,4), and (-2,4).

Answer: Student sketches y = x²

Question 6: Solve the system: x² + y = 9 and y = 3x - 1. (Use substitution)

Answer: x=2, y=5 or x=-2, y=-7

Question 7: A rectangular garden has a length of x meters and width of y meters. The area is given by y = x² - 4x + 3, and the perimeter is 20 meters. Find the dimensions of the garden.

Answer: x=1 or 3, y= (for x=1, y=-2; for x=3, y=0) — dimensions are x=3, y=0 or x=1, y=-2 (negative width indicates invalid, so x=3, y=0)

Question 8: Identify and correct the mistake: Solve x + y = 5 and y = x² + 1, but students incorrectly combine to x + x² + 1 = 5.

Answer: Incorrect; the correct approach is to substitute y from the second into the first: x + (x² + 1) = 5, leading to x² + x + 1=5, then solving for x.

Question 9: Challenge: Find the intersection points of y = x² - 4 and y = -x + 2.

Answer: x=1, y=-3 and x= -1, y=-3