CBSE Class 10 Answered

If the lines a1x+b1y+c1=0 and a2x+b2y+c2 = 0 has infinite number of solution then it must satisfy the condition -

                        a1/a2 = b1/b2 = c1/c2

      We have the lines,

                         (k-3)x + 3y = k
                         kx + ky = 12

         Therefore, we have:

                         k?3/k=3/k=k/12
                         12(k-3) = k(k)
                         12k?36=k^2
                         k^2?12k+36=0
                         (k?6)^2=0
                         k - 6 = 0
                         k = 6

Therefore the value of k is 6.