Consider the system of simultaneous equations cases x = k - 2y y = - 1 2 x + 2 cases .

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

Problem

Consider the system of simultaneous equations

\begin{cases} x = k - 2y \\ y = -\frac{1}{2}x + 2 \end{cases}.

(1) a** Find the gradient of each line. (2) b** Find the value(s) of

k

such that the system has: i no solutions ii infinitely many solutions. Interpret these cases geometrically.