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Question

Do the following equations represent a pair of coincident lines? Justify your answer.

3x+17y=3

7x+3y=7


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Solution

We know that the condition for coincident lines,

a1/a2=b1/b2=c1/c2;

The given pair of linear equations are:

3x+17y=3

7x+3y=7

On comparing the above equations with ax+by+c=0;

a1=3,b1=17,c1=3;

a2=7,b2=3,c2=7;

Now, a1/a2=3/7

b1/b2=1/21

c1/c2=3/7=3/7

Here,a1/a2b1/b2.

Hence, the given pair of linear equations does not represents a pair of coincident lines.


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