Simultaneous Equations

Understanding Simultaneous Equations

Simultaneous equations are a set of equations that share the same variables and are all satisfied by the same exact values of those variables.
The term simultaneous implies that the equations are solved together, at the same time.
Simultaneous equations may consist of two or more equations. However, the most common scenarios involve two equations with two unknown variables, often denoted as ‘x’ and ‘y’.
The goal is to find the values of the unknowns that satisfy all the equations at once.

There are commonly two methods used for solving simultaneous equations: the substitution method and the elimination method.
The substitution method involves rearranging one of the equations to make one variable the subject, and then replacing (substituting) this expression into the other equation.
The elimination method involves manipulating the equations so one variable cancels out when you subtract one equation from the other.
The choice of method often depends on the nature of the equations.
In some cases, simultaneous equations may be solved by graphing the equations, with the point of intersection representing the solution.

Always label your equations for clarity. It can help keep track of your steps.
Be patient with the algebraic manipulation required. Mistakes can effortlessly creep in.
Simplify each equation as much as possible to make the later steps easier.
Look for an opportunity to make the coefficients of ‘x’ or ‘y’ the same in both equations, if using the elimination method.
Make sure to always check your answers by substituting your solutions back into the original equations.

Problems can be translated into a set of simultaneous equations.
Be attentive when forming your equations: understand the problem and map the specified relationships properly.
Use your knowledge on solving simultaneous equations to find your solution.
As always, remember to check your solutions by substitifying them back into your formed equations.