# Equations and Systems with Two Variables

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