Question

: If a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are pair of linear equations in two variables they have no solution if​

Answer 1

Given :

A pair of linear equation,

• $\sf{a_{1}x+b_{1}y+c_{1}=0}$
• $\sf{a_{2}x+b_{2}y+c_{2}=0}$

To Find:

The condition for which they have no solution.

Concept Used:

A pair of linear equation have no solution if we plot their graph and it comes parallel lines ,since parallel lines never meet each other so ,they won't intersect each other ,and hence have no solution.

Solution:

A pair of linear equations will have no solution if

${\underline{\boxed{\red{\sf{\dfrac{a_{1}}{a_{2}}=\dfrac{b_{1}}{b_{2}}\neq \dfrac{c_{1}}{c_{2}}}}}}}$

Related Information:

→This type of solution is called inconsistent solutions

→ If we plot their graph ,it will come parallel lines.

→If the system had intersecting lines or concident lines ,then it has consistent solutions.

Answer 2

Answer:

equation a1x +b1y +c1=0 and a2x +b2y +C2=0 if a1/a2 is not equal toa1b2 a2b1 , then the system of equations a1x + b1y = c1 and a2x + b2y = c2.