Pair of linear equations in two variables


A pair of linear equations in two variables is said to form a system of simultaneous linear equations. The general form of a pair of linear equations in two variables x and y is:

a1x+ b1+ c1 =0

a2x+ b2+ c2 = 0,

where a1,b1,c1,a2,b2,c2,

are all real numbers and  a1+ b12 ≠ 0, a2+ b22 ≠ 0

Any pair of values of x and y which satisfies the pair of equations  a1x+ b1+ c1 =0, a2x+ b2+ c2 = 0 ,is called a solution. There are two methods: (i) Graphical Method, (ii) Algebraic Method, for finding the solution of pair of equations.

Let us discuss these two methods and find some important results about lines and solution.