Simultaneous Equations

• What is the first step in solving simultaneous equations according to the video?

  Label the equations as one and two
• What is the goal when solving simultaneous equations?

  To cancel one of the variables
• What should you multiply the first equation by to cancel y?

  Multiply by 5
• What should you multiply the second equation by to cancel y?

  Multiply by -2
• What is the lowest common denominator of 2 and 5?

  10
• What does the first equation become after multiplying by 5?

  15x + 10y = 5
• What does the second equation become after multiplying by -2?

  • 14x - 10y = 4
• Why can you multiply both sides of an equation by the same number?

  It keeps the equation equal
• What do you get when you add the modified equations together?

  x = 9
• After finding x, what should you do next?

  Substitute x back into an original equation
• What does the first equation become when substituting x = 9?

  27 + 2y = 1
• What is the value of 2y after rearranging the equation?

  2y = -26
• What is the final value of y after solving?

  y = -13
• What is the process for solving simultaneous equations?

  1. Label the equations.
  2. Multiply one or both equations to cancel a variable.
  3. Add the equations together.
  4. Substitute back to find the other variable.
• What should you remember when multiplying equations?

  • Multiply both sides by the same number.
  • Ensure one equation is positive and the other negative for cancellation.
• What are the key steps to remember for simultaneous equations?

  • Label equations to avoid confusion.
  • Use the lowest common denominator for multiplication.
  • Substitute back to find missing variables.