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Mathematics 4 ESO – Unit 5 SYSTEMS OF EQUATIONS extra activities

1 –  Watch the video on ” Solving Systems by Substitution”.

  • a) Why can we replace the “y” in the second equation for “(3x + 2)”?
  • b) After finding the value of “x”, how do we find the value of “y”?
  • c) Solve the system by substitution: y = 5x – 6  ;  6x + 2y = 4
  • d) Solve the system by substitution: 3x + 2y = 10  ;  x = -3y + 6

2 –  Watch the video on “Solving Systems of Equations”. The video explains how to solve a system of equations by addition (also called “elimination”).

    • a) To solve the system of equations, what is our first goal?
    • b) What do we do after cancelling out the “y” variable?
    • c) Solve the system by addition: 5x – y = 1  ;  6x + y = 10
    • d) Solve the system by addition: -x + 2y = 0  ;  x – 3y = -1

3 –  Watch the video on “Solve a System of Equations Using Eliminations”.

    • a) What are the different ways to solve systems of equations?
    • b) Why do we multiply both sides of the second equation by 3?
    • c) After finding the value of “x”, what do we do?
    • d) When we represent the system of equations graphically, what is the solution to the equation?
    • e) Solve the system by elimination (also called “addition”: 3x – y = 3  ;  x + y = 5   and verify the solution graphically.

4 –  Click on the link and watch the video on “Solving systems of linear equations — Basic example”.

  • a) In what case a system of linear equations has one solutions?
  • b) In what case a system of linear equations has no solution?
  • c) In what case a system of linear equations has infinite solutions?
  • d) In what case a system of linear equations has two solutions?
  • e) Why in this example we can’t have two solutions?
  • f) How do we know that the lines are going to have one solution?