Question 1: Given x + y = 10 and 2x - y = 4, find the values of x and y.

Answer: x=4, y=6

Question 2: Solve for x, y, z given the equations: x + y = 7, y + z = 9, and x + z = 10.

Answer: x=3, y=4, z=6

Question 3: If 3a + 2b = 12 and a - b = 1, find the values of a and b.

Answer: a=3, b=2

Question 4: Plot the graph of y = 2x + 3 for x values from -2 to 2.

Answer: See full answer key

Question 5: Construct a triangle with sides corresponding to the solutions of x + y = 8 and y + z = 10, choosing positive values for each variable.

Answer: See full answer key

Question 6: In a problem where x + y + z = 15, and x = 2y, z = y + 3, find the values of x, y, and z.

Answer: x=6, y=3, z=6

Question 7: Explain the mistake in solving the system: x + y = 5, x + y = 7. How would you correct it?

Answer: The mistake is assuming both equations are different but identical; they are inconsistent.

Question 8: Given the equations: 2x + 3y = 12 and 4x - y = 5, find the values of x and y using substitution.

Answer: x=2, y=4

Question 9: A car rental company charges a fixed fee plus a daily rate. If the total cost for 3 days is $150 and for 5 days is $210, find the fixed fee and daily rate.

Answer: fixed fee = $90, daily rate = $20

Question 10: Identify and correct the error in solving: x + 2y = 8, 3x + y = 11, when the student concludes x=2 and y=3.

Answer: The mistake is substituting incorrectly; the correct solution is x=1, y=3.

Question 11: Solve the system: x + y + z = 12, 2x - y + 3z = 10, and x - z = 3.

Answer: x=4, y=3, z=5