Mathematics

Problem

Consider the system of simultaneous equations

\begin{cases} 12 = 4x - cy \\ 2x + 6 = 3y \end{cases}

. Find the gradient of each line. a. Hence determine the value of

c

for which the simultaneous equations do *not* have a unique solution. Explain what is happening in this case. b. For any other value of

c

, the system has a unique solution. Find this solution in terms of

c