Question

Meaning of consistent and inconsistent pair of linear equations

Answer 1

Answer:

Consistent=lines intersect at point which represents the unique solution of the system of linear equations in two variables. Algebraically, if then, the linear equations' pair is consistent.

Inconsistent=lines which are parralel are inconsistent

Answer 2

1) has no solution or inconsistent

$\dfrac{a_{1}}{a_{2}} =\dfrac{b_{1}}{b_{2}}\neq \dfrac{c_{1}}{c_{2}}$

2) has a unique solution or consistent

$\dfrac{a_{1}}{a_{2}} \neq \dfrac{b_{1}}{b_{2}}$

Step-by-step explanation:

Consistent and inconsistent pair of linear equations

A system of linear equations:

$a_{1} x+b_{1} y+c_{1} =0$ and

$a_{2} x+b_{2} y+c_{2} =0$ is said to be consisten tif it has at least one solution. On the other hand, the above system is said to be inconsistent if it has no solution at all.

1) has no solution or inconsistent

$\dfrac{a_{1}}{a_{2}} =\dfrac{b_{1}}{b_{2}}\neq \dfrac{c_{1}}{c_{2}}$

2) has a unique solution or consistent

$\dfrac{a_{1}}{a_{2}} \neq \dfrac{b_{1}}{b_{2}}$