The shaded region in the provided graph repre | vedclass

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

Question

(C) $1$. Identify the boundary lines of the shaded region:- Line passing through $(1, 0)$ and $(0, 2)$: The equation is $\frac{x}{1} + \frac{y}{2} = 1

Vedclass · Accepted Answer

$2x + y \geq 2, x - y \leq 1, x + 2y \leq 8, x \geq 0, y \geq 0$

Vedclass · Answer

(C) $1$. Identify the boundary lines of the shaded region:- Line passing through $(1, 0)$ and $(0, 2)$: The equation is $\frac{x}{1} + \frac{y}{2} = 1$, which simplifies to $2x + y = 2$. Since the shaded region is above this line, the inequality is $2x + y \geq 2$.- Line passing through $(1, 0)$ and $(0, -1)$ (implied by the slope): The line passes through $(1, 0)$ and $(0, -1)$, so the equation is $y - 0 = \frac{-1 - 0}{0 - 1}(x - 1)$, which simplifies to $y = x - 1$ or $x - y = 1$. Since the shaded region is to the left of this line, the inequality is $x - y \leq 1$.- Line passing through $(0, 4)$ and $(4, 0)$ (implied by the intersection $B(10/3, 7/3)$): The line passing through $(0, 4)$ and $(4, 0)$ has the equation $\frac{x}{4} + \frac{y}{4} = 1$, which is $x + y = 4$. However, checking the intersection $B(10/3, 7/3)$ with $x + 2y = 8$, we see $10/3 + 2(7/3) = 10/3 + 14/3 = 24/3 = 8$. Thus, the line is $x + 2y = 8$. Since the shaded region is below this line, the inequality is $x + 2y \leq 8$.$2$. Combining these with $x \geq 0, y \geq 0$, we get the system: $2x + y \geq 2, x - y \leq 1, x + 2y \leq 8, x \geq 0, y \geq 0$.$3$. This matches option $C$.

The shaded region in the provided graph represents the solution set for which of the following systems of linear inequalities?

Similar Questions

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: $3x + y > 0$ and $3x + y < 3$.

The shaded region in the provided graph represents the solution set for which of the following systems of linear inequalities?

Solve the following system of linear inequalities: $x+5 > 2(x+1)$ and $2-x < 3(x+2)$.

The region represented by the inequalities $x \geq 6, y \geq 3, 2x + y \geq 10, x \geq 0, y \geq 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module

The shaded region in the provided graph represents the solution set for which of the following systems of linear inequalities?

Similar Questions

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: $3x + y > 0$ and $3x + y < 3$.

The shaded region in the provided graph represents the solution set for which of the following systems of linear inequalities?

Solve the following system of linear inequalities: $x+5 > 2(x+1)$ and $2-x < 3(x+2)$.

The region represented by the inequalities $x \geq 6, y \geq 3, 2x + y \geq 10, x \geq 0, y \geq 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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