An equation which can be put in the form ax + by + c = 0,where a, b and c are real numbers, and a and b are not both zero, is called a  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique in two variables x and y.

Two linear equations in the same two variables are called a  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique in two variables.

A pair of linear equations which has no solution, is called an  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique pair of linear equations.

A pair of linear equations in two variables, which has a solution, is called a  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique pair of linear equations.

A pair of linear equations which are equivalent has  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique many distinct common solutions. Such a pair is called a  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique pair of linear equations in two variables.

If the lines intersect at a point, then that point gives the  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique solution of the two equations.

If the lines coincide, then there are  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique solutions — each point on the line being a solution.

If the lines are parallel, then the pair of equations has  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique solution.

(a₁⁄a₂)≠(b₁⁄b₂)-In this case, the pair of linear equations is  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique.

(a₁⁄a₂)=(b₁⁄b₂)≠(c₁/c₂)-: In this case, the pair of linear equations is  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique.

(a₁⁄a₂)=(b₁⁄b₂)=(c₁/c₂) In this case, the pair of linear equations is  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique.

If a pair of linear equations is consistent then the lines will be  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique.

If a pair of linear equations is inconsistent then the lines will be  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique.

The pair of equations x = 2 and y = - 2 has  consistentdependentdependent and consistentinconsistentinfinitelyinfinitely manyIntersect or coincidentlinear equationnoonepair of linear equationsparallelunique solution.