The shaded region in the figure is the soluti | vedclass

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

Question

(D) $1$. The line passing through $A(7, 0)$ and $(0, 7)$ has the equation $\frac{x}{7} + \frac{y}{7} = 1$,which simplifies to $x + y = 7$. Since the s

Vedclass · Accepted Answer

$x+y \leq 7, 2x-3y+6 \geq 0, x \geq 0, y \geq 0$

Vedclass · Answer

(D) $1$. The line passing through $A(7, 0)$ and $(0, 7)$ has the equation $\frac{x}{7} + \frac{y}{7} = 1$,which simplifies to $x + y = 7$. Since the shaded region is towards the origin,the inequality is $x + y \leq 7$.$2$. The line passing through $C(0, 2)$ and $B(3, 4)$ has the slope $m = \frac{4-2}{3-0} = \frac{2}{3}$. The equation is $y - 2 = \frac{2}{3}(x - 0)$,which simplifies to $3y - 6 = 2x$,or $2x - 3y + 6 = 0$. Testing the point $(3, 0)$ which is in the shaded region: $2(3) - 3(0) + 6 = 12 \geq 0$. Thus,the inequality is $2x - 3y + 6 \geq 0$.$3$. Since the region is in the first quadrant,$x \geq 0$ and $y \geq 0$.$4$. Combining these,the system is $x + y \leq 7, 2x - 3y + 6 \geq 0, x \geq 0, y \geq 0$. Therefore,option $(D)$ is correct.

The shaded region in the figure is the solution of which of the following systems of inequations?

Similar Questions

Solve for $x$ the following system of inequalities: $|x-1| \leq 5$ and $|x| \geq 2$.

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

Solve the following system of inequalities graphically: $x+y \geq 4, 2x-y > 0$.

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

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module