Simultaneous Equations & Linear Equation in 2 Variables

A set of 2 (or more) linear equations in 2 (or more) variables which are satisfied simultaneously by a same unique solution are called as Simultaneous Equations.
e.g. 2x + 3y = 14
and 2x – 3y = 2
The two equations above are satisfied by a unique solution (4,2). Hence these are simultaneous equations.

Linear Equation in 2 Variables
An equation of the form ax+by = c where a,b,c are real numbers is called linear equation in two variables.
The value of x and y which satisfies this equation, i.e. both sides of the equation becomes equal, is called the solution of the equation.

Example :
2x + 3y = 14
The value x = 4 and y = 2 satisfies the equation. So, (4,2) is a solution of this equation.
The value x = 1 and y = 4 also satisfies the equation & hence is a solution of this equation.
The value x = -2 and y = 6 also satisfies the equation & hence is a solution of this equation.

We can visualize that there may be infinite number of solution for the above equation. So, a linear equation in two variables will not have a unique solution, it will have infinite number of a solution.

If we draw a graph of the linear equation in two variables, all the infinite points lying on the line will represent a solution of the equation.
Let’s draw a graph of line 2x + 3y = 14 below.