Subject 1: The equation ax + by = c, the solution as a pair, the solution set, the graph of a linear equation.

• Level 1 : Is the pair (2, -5) a solution of the equation 2x - 3y = - 6 ?
• Level 2 : Find y such that the pair (-3/4, y) is a solution of -2x + y = 4
• Level 3 : Express y in terms of x in the equation -x - 7y = 5

Subject 2: Solving a system of two linear equations graphically

• Level 1 : Solve, by the graphic method, a system such as:
  -3x + 3y = 5
  4x - 2y = -7

Subject 3: The substitution and the addition methods.

• Solve the system by an algebraic method (addition or substitution)
• Level 1 :
  -x + 3y = 5
  4x - 2y = -7
• Level 2 :
  2(-x + 3y) - 3(x - 5) = 5y + 1
  4x - 21 + y - 2 = -7(3x - 7y)
• Level 3 :
  (-2x - 3)/4 = (-x + 5y)/7
  4x - 2y = -1

Subject 4: Special systems with no solution or dependent equations, investigating a system with a parameter.

• Level 1 : Finding the number of solutions of a system
• Level 2 : For which value of m the following system does not have a unique solution :
  (4 - m)x + 2y = 4
  (4m + 2)x - y = 10