Question

A system of two linear equations in two variables is dependent consistent, if their graphs

Answer 1

A system of two linear equations in two variables is dependent consistent if the lines are coincident.

Solution: A system of two linear equations is consistent when it has at least one solution.

It is dependent consistent only when it has infinitely many solutions.

For two linear equations ax+by+c=0 and px+qy+r=0 to have infinitely many solutions, the necessary condition is:

$\frac{a}{p} = \frac{b}{q} = \frac{c}{r}$

When these lines are drawn on a graph paper, the lines are completely coincident implying that the equations represent the same line in the plane.