Question

For what value of k the system of equation kx + 3 y is equal to 12 x + k y is equal to 2 has no solution

Answer 1

Answer:

Question;

For what value of k the system of equations;

kx+3y = 12 and x+ky = 2

has no solution.

Solution:-

Note;

If we consider two lines;

(a1)x + (b1)y + (c1) = 0 and

(a2)x + (b2)y + (c2) = 0,

Then, the condition for no solution

( or condition for lines to be parallel) is;

a1/a2 = b1/b2 ≠ c1/c2.

We have;

The given system of line as;

kx + 3y = 12 and x + ky = 2

where:

a1=k and a2=1

b1=3 and b2=k

c1=12 and c2=2

Here, it is clear that, c1≠c2,

Thus, the system of given pair of lines will have no solution if and only if;

=> a1/a2 = b1/b2

=> k/1 = 3/k

=> k^2 = 3

=> k = ± √3

Thus, the required values of k are ;

√3 and - √3