Applied Simultaneous Linear Equations

What Are Simultaneous Linear Equations?

Simultaneous linear equations are a set of two or more linear equations with the same variables. The solution to these equations is the set of values that satisfy all the equations at the same time.

Why Are They Important?

Simultaneous equations are used to solve real-life problems where two conditions must be met simultaneously. For example, finding the point where two lines intersect on a graph.

Methods to Solve Simultaneous Equations

• Substitution Method: Solve one equation for one variable and substitute this into the other equation.
• Elimination Method: Add or subtract equations to eliminate one variable, making it easier to solve for the other.
• Graphical Method: Plot both equations on a graph and find the intersection point.

Worked Example: Solving Simultaneous Equations

Example Problem

Solve the following simultaneous equations:

• Equation 1: $3x + 4y = 18$
• Equation 2: $2x - y = 3$