Question

Write all condition for a pair of linear equations in two variables for consistent and inconsistent

Answer 1

Answer:

Step-by-step explanation:$\frac{a}{h}=  \frac{b}{j}=\frac{c}{d}$

let two equations be ax+by=c & hx+jy=d

case 1 :

if $\frac{a}{h}\neq  \frac{b}{j}$

system will have only one solution and system will be consistent.

case 2 :

if $\frac{a}{h}=  \frac{b}{j}=\frac{c}{d}$

system will have infinitely many solution so system is consistence

case 3 :

if $\frac{a}{h}=  \frac{b}{j}\neq \frac{c}{d}$

it represents two parallel lines. so no solution for two given lines.

so system will be inconsistent.

Answer 2

Answer:

To compare equations in linear systems, the best way is to see how many solutions both equations have in common. If there is nothing common between the two equations then it can be called as inconsistent. But it will be called consistent if any one ordered pair can solve both the equations.