Question

Select the region that represents the solution​

Answer 1

D.

Explanation:

`<,\ \leq-\text{shaded at the bottom of the line}\\>,\ \geq-\text{shaded at the top of the line}\\--------------------------------\\\text{Calculate the y-intercept. Put x = 0.}\\\\4x-2y\leq0\to4(0)-2y=0\\\\-2y=0\qquad\text{divide both sides by (-2)}\\\\y=0\\\\5x+3y\leq-11\to5(0)+3y=-11\\\\3y=-11\qquad\text{divide both sides by 3}\\\\y=-(11)/(3)\to y=-3(2)/(3)`

`\text{Now specify on which side of the line we are shading.}\\\\4x-2y\leq0\qquad\text{add}\ 2y\ \text{to both isdes}\\\\4x\leq2y\qquad\text{divide both sides by 2}\\\\2x\leq y\to y\geq2x\to\text{shaded at the top of the line}\\------------------------\\5x+3y\leq-11\qquad\text{subtract 5x from both sides}\\\\3y\leq-5x-11\qquad\text{divide both sides by 3}\\\\y\leq-(5)/(3)x-(11)/(3)\to\text{shaded at the bottom of the line}`

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