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# The set of all solutions of the system

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The set of all solutions of the system

x + y <= 4

2x + y >= 5

x >= 0

y >= 0

is a quadrilateral region. Find the number of units in the length of the longest side. Express your answer in simplest radical form.

Nov 5, 2020

### 1+0 Answers

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The set of all solutions of the system

Hello Guest!

1)

$$1)\\ y <= 4\\ 2x + y >= 5\\ 2)\ x >= 0\\ 3)\ y >= 0$$

1)

$$x + y \le 4$$             $$1+3\le4$$

$$2x+y\ge 5$$           $$2\cdot1+3\ge 5$$

$$y=4-x\\ y=5-2x\\ 4-x=5-2x\\ 2x-x=5-4$$

$$x=1\\ y=3$$

2)

$$x \ge 0$$

$$x\in| \mathbb {Q}|$$

3)

$$y\ge 0$$

$$y\in| \mathbb {Q}|$$

!

Nov 6, 2020
edited by asinus  Nov 6, 2020