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Question

(C) $1$. Identify the boundary lines of the shaded region:- Line passing through $(0, 2)$ and $(1, 0)$: 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 $(0, 2)$ and $(1, 0)$: The equation is $\frac{x}{1} + \frac{y}{2} = 1 \implies 2x + y = 2$. Since the shaded region is above the line, the inequality is $2x + y \geq 2$.- Line passing through $(1, 0)$ and $(10/3, 7/3)$: The slope $m = \frac{7/3 - 0}{10/3 - 1} = \frac{7/3}{7/3} = 1$. The equation is $y - 0 = 1(x - 1) \implies x - y = 1$. Since the shaded region is to the left of the line, the inequality is $x - y \leq 1$.- Line passing through $(0, 4)$ and $(10/3, 7/3)$: The slope $m = \frac{7/3 - 4}{10/3 - 0} = \frac{-5/3}{10/3} = -1/2$. The equation is $y - 4 = -1/2(x - 0) \implies 2y - 8 = -x \implies x + 2y = 8$. Since the shaded region is below the line, the inequality is $x + 2y \leq 8$.$2$. The non-negativity constraints are $x \geq 0, y \geq 0$.$3$. Combining these, the system is $2x + y \geq 2, x - y \leq 1, x + 2y \leq 8, x \geq 0, y \geq 0$. This matches option $C$.

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

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