Simultaneous equations

• What are simultaneous equations?

  Equations with more than one unknown that can have infinite solutions
• How can the equation $2x +$$y =$$10$ be solved?


  By finding pairs of values such as $(3, 4)$ and $(2, 6)$
• What is required to solve a simultaneous equation?

  Another equation alongside it to find the only pair of values
• What is the most common method for solving simultaneous equations?

  The elimination method
• What does the elimination method involve?

  Moving one of the unknowns from each equation to calculate the remaining one
• When can the elimination method be applied?

  When the coefficients of the unknowns are the same in each equation
• In the example, what is the first step to eliminate $y$ from the equations $3x +$$y =$$11$ and $2x +$$y =$$8$?


  Identify that $y$ has a coefficient of 1
• How do you find the value of $y$ after substituting $x =$$3$?


  Perform inverse operations on each side to solve for $y$
• What is a quadratic equation?

  An equation where the highest power is 2
• What is a linear equation?

  An equation that doesn't contain any powers higher than 1
• Give an example of a linear equation.

  $y =$$x +$$1$
• Give an example of a quadratic equation.

  $y =$$x^2 +$$3x$
• How many pairs of answers will there always be when solving simultaneous equations involving linear and quadratic equations?

  Two pairs of answers
• What is the solution point in graphical methods of solving simultaneous equations?

  The coordinate point where the two graphs cross one another
• What are the steps to solve the equations $x +$$y =$$5$ and $y =$$x +$$1$ graphically?


  Draw axes, plot graphs, and find the coordinate point
• What is the coordinate point for the equations $x +$$y =$$5$ and $y =$$x +$$1$?


  The coordinate point is $(2, 3)$
• What are the methods for solving simultaneous equations?

  • Algebraically (elimination and substitution)
  • Graphically (plotting graphs)
• What are the key differences between linear and quadratic equations?

  • Linear equations: highest power is 1
  • Quadratic equations: highest power is 2
• How do you solve simultaneous equations using the elimination method?

  1. Identify coefficients of unknowns
  2. Add or subtract equations to eliminate one unknown
  3. Solve for the remaining unknown
  4. Substitute back to find the eliminated unknown