Mathematics » Equations and Inequalities » Solving Simultaneous Equations

Solving Simultaneous Equations

Solving Simultaneous Equations

Up to now we have solved equations with only one unknown variable. When solving for two unknown variables, two equations are required and these equations are known as simultaneous equations. The solutions are the values of the unknown variables which satisfy both equations simultaneously. In general, if there are $$n$$ unknown variables, then $$n$$ independent equations are required to obtain a value for each of the $$n$$ variables.

An example of a system of simultaneous equations is:

\begin{align*} x + y & = -1 \\ 3 & = y – 2x \end{align*}

We have two independent equations to solve for two unknown variables. We can solve simultaneous equations algebraically using substitution and elimination methods. We will also show that a system of simultaneous equations can be solved graphically.