Question

Find value of k for infinite Sol for pair of linear equation

kx + 3y = 2k + 1

2 ( k + 1)x + 9x = 7k + 1

Answer 1

We have an infinite number of solutions if the 2 equations are basically the same equation
We have
kx + 3y = 2k + 1 (1)
2 ( k + 1)x + 9y = 7k + 1 (2)
If we multiply (1) by 3 both equations will have +9y
3kx+9y=6k+3 and
(2k+2)x +9y = 7k+1
For the equations to be the same, the coefficeints of x and right hand side must also be equal
Thus 3k = 2k+2 => k = 2
and 6k+3= 7k+1=> k = 3-1 = 2
So k= 2 makes both equations the same and hence to have infinte number of solutions

Answer: k = 2