Solve the following system of inequalities graphically: $2x - y > 1, x - 2y < -1$

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) $2x - y > 1$ ..... $(1)$
$x - 2y < -1$ ..... $(2)$
The graph of the lines,$2x - y = 1$ and $x - 2y = -1$,are drawn in the figure below.
Inequality $(1)$ represents the region below the line $2x - y = 1$ (excluding the line $2x - y = 1$),and inequality $(2)$ represents the region above the line $x - 2y = -1$ (excluding the line $x - 2y = -1$).
Hence,the solution of the given system of linear inequalities is represented by the common shaded region excluding the points on the respective lines as shown in the figure.

Explore More

Similar Questions

Solve the following system of inequalities graphically: $3x + 2y \leq 12, x \geq 1, y \geq 2$

The set $\{x \in R: \frac{14x}{x+1} - \frac{9x-30}{x-4} < 0\}$ is equal to

Solve the following system of inequalities graphically:
$x + 2y \leqslant 8$ ..... $(1)$
$2x + y \leqslant 8$ ..... $(2)$
$x \geqslant 0$ ..... $(3)$
$y \geqslant 0$ ..... $(4)$

Solve the following system of inequalities graphically: $x+y \leq 9, y>x, x \geq 0$.

The shaded region shown in the figure is given by the inequations:

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo