Question

Write consistent pair of linear equation in two variable

Answer 1

If both the lines intersect at a point, then there exists a unique solution to the pair of linear equations. In such a case, the pair of linear equations is said to be consistent.

Algebraically, if a1a2 ≠ b1b2a1a2 ≠ b1b2 then, the linear equations’ pair is consistent.

Answer 2

<br> Algebraically, if a1a2 ≠ b1b2 then, the linear equations’ pair is consistent.  i) Consider two lines having equation to be-  a1x+b1y+c1 = 0 and  a2x+b2y+c2 = 0  Let these lines coincide with each other, then there exist infinitely many solutions since a line consists of infinite points. In such a case, the pair of linear equations is said to be dependent and consistent. As represented in the graph below, the pair of lines are coincident and therefore, dependent and consistent.