Solve the following system of inequalities \(\dfrac{2x+1}{7x-1} > 5\) and \(\dfrac{x+7}{x-8} > 2\).
No Solution
Find the linear inequalities for which the shaded region in Fig 6.5 is the solution set. (The figure shows a triangular/ trapezoidal shaded region bounded by the lines \(x+y=20\), \(3x+2y=48\), the x-axis and the y-axis.)
\(x + y \le 20,\)
\(3x + 2y \le 48,\)
\(x \ge 0,\; y \ge 0\)
Find the linear inequalities for which the shaded region in Fig 6.6 is the solution set. (The figure shows a rectangular/ trapezoidal shaded region bounded by the lines \(x+y=8\), \(x+y=4\), \(x=5\), \(y=5\), and the coordinate axes.)
\(x + y \le 8,\)
\(x + y \ge 4,\)
\(x \le 5,\; y \le 5,\; x \ge 0,\; y \ge 0\)
Show that the following system of linear inequalities has no solution: \(x + 2y \le 3,\; 3x + 4y \ge 12,\; x \ge 0,\; y \ge 1\).
Solve the following system of linear inequalities: \(3x + 2y \ge 24,\; 3x + y \le 15,\; x \ge 4\).
No Solution
Show that the solution set of the following system of linear inequalities is an unbounded region: \(2x + y \ge 8,\; x + 2y \ge 10,\; x \ge 0,\; y \ge 0\).