Subject 1: Solving a quadratic system. The graphic interpretation.

• Solve systems such as the following by the substitution method:
• Level 1 :
  -3x - y = 5
  4x² - 2y = 14
• Level 2 :
  2x - 3y = -7
  -2x² - 3xy + y² = -1

Subject 2: Investigating a linear equation with a parameter.

• In the following equations, x is the unknown, m is a parameter:
• Level 1 : Write the equation of the family 2mx - 1 = x + m when m = 4
• Level 2 : Find the value of m given that x = 2/3 is solution of the equation 2m - x = x + m
• Level 3 : Solve the equation 2mx - 1 = m + x
• Level 4 : Express t in terms of the other variables in v = at + 3

Subject 3: Solving a linear system with a parameter.

• For which value of m, the system has no unique solution?
  Use either the addition method or the substitution method and solve the system
• Level 1 :
  -3mx + 5y = 3
  5x + 2y = -7
• Level 2 :
  4x + 5y = 3m
  (2m - 1)x + 2y = -7