Consider the system of simultaneous equations

MATHEMATICS · Multi-part · CBSE · Mathematics · Pair of Linear Equations in Two Variables · Pair of Linear Equations in Two Variables

Problem

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

. Find the gradient of each line. (1) Hence determine the value of

c

for which the simultaneous equations do *not* have a unique solution. Explain what is happening in this case. (2) For any other value of

c

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

c