To know the type of equations:

The equation can only be solved if the number of equations is equal to the number of variables. As if the equation has two variable x and y then to find the answer of these you should have two such equations.

Now, the two equations can have three types of solutions as they could be:

Parallel, Coincide and Intersecting.

For Parallel equations, there is no solution as these equations have no common point and are also called as Inconsistent.

Coincide & Intersecting lines are Consistent.

Coincide equation are those which overlap each other, and this type of equations has infinitely many solutions whereas intersecting lines intersect on one common point and thus have (accurately) One solution.

Type of equation can be identified by comparing the ratios of there coefficients,

1. If the ratio of the first variable of two equations is not equal to the ratio of the second variable of two equations, then these are Intersecting lines: a1/a2 =! b1/b2.

2. If the ration of all the variables is equal to two equations, then these are Coincide lines :

a1/a2 = b1/b2 = c1/c2

3. If the ratio of the first variable of two equations is equal to the ratio of the second variable of two equations but not equal to the ratio of the third variable of two equations then these are known as Parallel lines :

a1/a2 = b1/b2 =! c1/c2.

Try to understand the type of equation by comparing the ratio of coefficients of variables. (Keep in mind the general equation: ax+by+c=0 where a is coefficient of x, b is coefficient of y and c is constant).