## Mathematical Topics: Equations 3 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        (C) Copyright 2000 MathKal Educational Software Ltd.