3.6 Solution of Simultaneous Linear Equations

3.6 Solution of Simultaneous Linear Equations

A linear equation is an algebraic equation in which the highest power of the variable is $1$. A general form of a linear equation in two variables is:

$ax + by = c$, where $a, b, c$ are real numbers, $x$ and $y$ are variables and $a, b \neq 0$.

Simultaneous linear equations are a set of two or more linear equations with two or more variables that are solved together (simultaneously) to find a common solution.

The general form of system of two linear equations in two variables is given below:

$ax + by = m$

$cx + dy = n$

where $a, b, c, d, m$ and $n$ are real numbers.

Here, we will find the solution of two simultaneous equations in two variables by the following methods:

(i) Matrix Inversion Method
(ii) Cramer's Rule