Pair of Linear Equations in Two Variables

A pair of linear equations

A pair of linear equations in two variables is written as a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, where a1, b1, c1 and a2, b2, c2 are constants and

A pair is consistent if it

A pair is consistent if it has a solution. It is inconsistent if it has no solution. A dependent pair has infinitely many distinct common solutions an

Intersecting lines give one solution

Intersecting lines give one solution, parallel lines give no solution, and coincident lines give infinitely many solutions.

If a1/a2 ≠ b1/b2

If a1/a2 ≠ b1/b2, the lines intersect. If a1/a2 = b1/b2 = c1/c2, the lines are coincident. If a1/a2 = b1/b2 ≠ c1/c2, the lines are parallel.

Two straight lines are drawn from

Two straight lines are drawn from the equations. Their point of intersection gives the solution. If they overlap, there are infinitely many solutions;