Simultaneous Equations

Understanding Simultaneous Equations

  • Simultaneous equations are a set of equations with multiple variables.
  • They are named “simultaneous” because they must all be true at the same time.

Solving Simultaneous Equations

  • To solve them, you need to find the values of the variables that satisfy all equations in the set.
  • The two main methods for solving are Substitution and Elimination.

Substitution Method

  • The substitution method involves rearranging one equation to express one variable in terms of the other, and then substituting this into the other equation.

Elimination Method

  • The elimination method involves adding or subtracting the equations in order to eliminate one of the variables.
  • It is often easier to use this method when the coefficients of one of the variables are the same or additive inverses in the two equations.

Practice and Review

  • It’s essential to practice solving simultaneous equations and check your answers by substituting the found values back into the original equations.
  • It’s helpful to remember that the number of variables equals the number of equations needed to solve for all variables.
  • For more complex sets of equations, other methods such as substitution could be more straightforward.

Real Life Application

  • Simultaneous equations are used in numerous real-life situations, such as business and finance to model and solve problems. Therefore, understanding this topic contributes not only to exam success but also to functional numeracy skills.