Question

write the condition for a pair of linear equation a 1 X + b 1 y + c1 is equal to zero and a2 X +b 2 y +c 2 is equal to zero are consistent on the basis of coefficients
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Answer 1

Answer:

a1 / a2 = b1/ b2 = c1/c2

Step-by-step explanation:

As they represent coincident lines this is the answer :)

Answer 2

Answer:

For $a$ pair of linear equation to be consistent:

1) $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$           2) $\frac{a_1}{a_2} = \frac{b_1}{b_2}=\frac{c_1}{c_2}$

Step-by-step explanation:

Given:-

A pair of linear equation are $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$.

To find:-

The condition for which given pair of equations are consistent.

As we know,

A pair of linear equation is said to be consistent if there exists at least one solution.

Case1. When solution is unique.

The condition on the basis of coefficients will be,

$\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$

Thus, the lines are intersecting and have a unique solution.

Hence, a pair of linear equations is consistent.

Case2. When infinite many solution.

The condition on the basis of coefficients will be,

$\frac{a_1}{a_2} = \frac{b_1}{b_2}=\frac{c_1}{c_2}$

Thus, the lines are coincident and have infinite many solutions.

Hence, a pair of linear equations is consistent.

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