Question

For what value of 'K', the following pair of linear equations have no solution?
3x - y-5=0
6x - 2y +K=0

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Answer 1

Step-by-step explanation:

Given:-

3x - y-5=0

6x - 2y +K=0

To find:-

For what value of 'K', the following pair of linear equations have no solution?

3x - y-5=0

6x - 2y +K=0

Solution:-

Given equations are 3x - y-5=0 and

6x - 2y +K=0

We have,

a1 = 3, b1 =-1 and c1 = -5

a2 = 6 ,b2 = -2 and c2 = k

we know that

a1x+b1y+c1=0 and a2x+b2y +c2=0 are the pair of linear equations in two variables ,

if a1/a2 = b1/b2≠c1/c2 then they have no solution.

3/6 = -1/-2≠-5/k

=>1/2=1/2≠-5/k

=>1/2 ≠-5/k

On applying cross multiplication then

=>k×1 ≠-5×2

=>k≠-10

Answer:-

The value of k is not equal to -10 then they have no solution .

Note:-

If k=-10 then they are dependent lines with infinitely number of many solutions.

Used Formula:-

• a1x+b1y+c1=0 and a2x+b2y +c2=0 are the pair of linear equations in two variables ,
• if a1/a2 = b1/b2≠c1/c2 then they have no solution.

Additional information:-

a1x+b1y+c1=0 and a2x+b2y +c2=0 are the pair of linear equations in two variables ,

• if a1/a2 = b1/b2≠c1/c2 then they have no solution.
• if a1/a2 ≠b1/b2≠c1/c2 then they have only one solution.
• if a1/a2 = b1/b2=c1/c2 then they have infinitely number of many solutions .