Question

 If a pair of linear equations is consistent, then the lines will be:

(A) Parallel                                         

(B) Always coincident

(C) Intersecting or coincident            

(D) Always intersecting​

Answer 1

Answer:

If a pair of linear equations is consistent, then the lines will be:

(A) Parallel                                         

(B) Always coincident

(C) Intersecting or coincident            

(D) Always intersecting

Answer 2

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A pair of Straight Lines

$\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$

Is said to be consistent if

$\displaystyle \: \: \frac{a_1}{a_2} \ne \frac{b_1}{b_2}$ or $\displaystyle \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2}=\frac{c_1}{c_2}$

Again the condition for two linear equations

$\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$

be always intersecting is

$\displaystyle \: \: \frac{a_1}{a_2} \ne \frac{b_1}{b_2}$

Also The condition for pair of linearequations $\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$

to be coincident is

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

Hence

 If a pair of linear equations is consistent, then the lines will be

(C) Intersecting or coincident