# 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.