Question

There is (are) ______ value(s) of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 have infinitely many solutions.

Answer 1

There is (are) no value(s) of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 have infinitely many solutions.

Explanation:

For infinitely many solutions the coefficients and constants must be proportional:

`c/6 = (-1)/(-2) = 2/3`

But `(-1)/(-2) = 1/2`, so `c/6` would have to equal `1/2 → c = 3`, while `2/3 ≠ 1/2`. 

The three ratios cannot be equal for any c, so no value of c gives infinitely many solutions.