The shaded region in the following figure rep | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The shaded region is bounded by the lines $x-y=0$ and $x+y=0$. For the line $x-y=0$,testing a point in the shaded region,such as $(1, 0)$,gives $1

Vedclass · Accepted Answer

$x-y \leq 0, x+y \geq 0$

Vedclass · Answer

(A) The shaded region is bounded by the lines $x-y=0$ and $x+y=0$. For the line $x-y=0$,testing a point in the shaded region,such as $(1, 0)$,gives $1-0=1 > 0$. However,the region includes the line itself,so we consider $x-y \leq 0$ for the region below the line $y=x$. Looking at the graph,the shaded region lies below the line $y=x$ (i.e.,$y \geq x$ or $x-y \leq 0$) and above the line $y=-x$ (i.e.,$y \geq -x$ or $x+y \geq 0$). Thus,the inequalities representing the shaded region are $x-y \leq 0$ and $x+y \geq 0$.

The shaded region in the following figure represents the solution set of:

Similar Questions

Solve the following system of inequalities graphically: $x - y + 2 \geq 0$ and $2x + y - 5 \leq 0$.

The region satisfying the inequalities $y - x \geq 2$, $x + y \leq 5$, $x \geq 0$ and $y \geq 0$ is

Solve the following system of inequalities graphically: $3x + 4y \leq 60, x + 3y \leq 30, x \geq 0, y \geq 0$

Find the linear inequalities for which the shaded region in the given figure is the solution set.

Solve the following system of inequalities graphically: $2x + y \geq 8, x + 2y \geq 10$

Vedclass Test Series

Exam Paper Generator

Online Exam Module