• # question_answer How many values of c, for which the system of equations $6x+3y=c-3,\text{ }12x+cy=c$ has infinitely many solutions? A)  1                                B)  2                    C)         3                    D)         Infinite

Given equations are $6x+3y=c-3$ and $12x+cy=c$ For infinitely many solutions, $\frac{6}{12}=\frac{3}{c}=\frac{c-3}{c}$ Taking first two members, we have             $\frac{1}{2}=\frac{3}{c}\,\,\Rightarrow \,\,c=6$ Thus, only one value of c exists.