Question

The pair of linear equation k X + 2 y is equal to 5 and 3 X + y is equal to one has unique solution if

Answer 1

Answer:

Note;

If we consider a pair of linear equations in two variables, say ;

a1x + b1y + c1 = 0 and

a2x + b2y + c2 = 0

The condition for unique solution is;

a1/a2 ≠ b1/b2

Here,

The given pair of linear equations is;

kx + 2y = 5 OR kx + 2y - 5 = 0

3x + y = 1 OR 3x + y - 1 = 0

Clearly, here we have;

a1 = k

a2 = 3

b1 = 2

b2 = 1

c1 = -5

c2 = -1

Thus, for unique solution we have;

=> a1/a2 ≠ b1/b2

=> k/3 ≠ 2/1

=> k ≠ 2•3

=> k ≠ 6

Hence, for unique solution of the given pair of linear equations, k can take place of any real value except 6.

Answer 2

Answer:

: Solution :

= Suppose the linear equation in two variables :

= a1x + b1y + c1 = 0 .

= a2x + b2y + c2 = 0.

= For unique solution :

= a1/a2 ≠ b1/b2

= According to question :

= The pair of linear equation

= kx + 2y = 5 and kx + 2y - 5 = 0 .

= 3x + y = 1 and 3x + y - 1 = 0 .

= Thus we have :

a1 = k. b1 = 2 . c1 = -5.

a2 = 3. b2 = 1 . c2 = -1.

= For unique solution we have :

= a1/a2 ≠ b1/b2 .

= k/3 ≠ 2/1.

= k ≠ 2/3.

= k ≠ 2 × 3.

= k ≠ 6 .