Question

For what value of k the pair of linear equations 3 X + Y = 3 and 6 X + k y =8 does not have a solution.​

Answer 1

Step-by-step explanation:

Given :-

3 X + Y = 3 and 6 X + k y =8

To find :-

For what value of k the pair of linear equations 3 X + Y = 3 and 6 X + k y =8 does not have a solution ?

Solution :-

Given pair of linear equations in two variables are

3 X + Y = 3

=> 3 X + Y - 3 = 0

On comparing with a1x+b1y+c1 = 0 then

a1 = 3

b1 = 1

c1 = -3

and 6 X + k y =8

=> 6X + kY - 8 = 0

On comparing with a2x+b2y+c2=0 then

a2 = 6

b2=k

c2 = -8

We know that

The pair of linear equations in two variables a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are inconsistent then they have no solution.

=> a1/a2 = b1/b2

=> 3/6 = 1/k

=> 1/2 = 1/k

=> 2 = k

Therefore, k = 2

Answer:-

The required value of k for the given problem is 2

Used formulae:-

• If a1/a2 = b1/b2 then they have no solution.

Additional information:-

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

• If a1/a2 ≠b1/b2≠c1/c2 then they are consistent and independent lines or intersecting lines with a unique solution.

• If a1/a2 = b1/b2 = c1/c2 then they are consistent and dependent lines or coincident lines with infinitely number of many solutions.

• If a1/a2 = b1/b2≠c1/c2 then they are inconsistent or Parallel lines with no solution.

Answer 2

I think this is useful for u..