Solve the following systems of inequations graphically: $x - 2 y \leq 2, x + y \geq 3, - 2 x + y \leq 4, x \geq 0, y \geq 0$

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Inequality Equation x coordinate y coordinate Line passes through (x,y) Sign of inequality Region
$x - 2 y \leq 2$ $x - 2 y = 2$ 2 0 $(2, 0)$ $\leq$ Origin side
0 -1 $(0, - 1)$
$x + y \geq 3$ $x + y = 3$ 3 0 $(3, 0)$ $\geq$ Non origin side
0 3 $(0, 3)$
$- 2 x + y \leq 4$ $- 2 x + y = 4$ -2 0 $(- 2, 0)$ $\leq$ Origin side
0 4 $(0, 4)$

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Inequality	Equation	x coordinate	y coordinate	Line passes through (x,y)	Sign of inequality	Region
$x - 2 y \leq 2$	$x - 2 y = 2$	2	0	$(2, 0)$	$\leq$	Origin side
		0	-1	$(0, - 1)$
$x + y \geq 3$	$x + y = 3$	3	0	$(3, 0)$	$\geq$	Non origin side
		0	3	$(0, 3)$
$- 2 x + y \leq 4$	$- 2 x + y = 4$	-2	0	$(- 2, 0)$	$\leq$	Origin side
		0	4	$(0, 4)$

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Inequality Equation x coordinatey coordinate Line passes through (x,y)Sign of inequality Region x−2y≤2 x−2y=2 2 0 (2,0) ≤ Origin side 0 -1 (0,−1) x+y≥3 x+y=3 3 0 (3,0) ≥ Non origin side 0 3 (0,3) −2x+y≤4 −2x+y=4 -2 0 (−2,0) ≤ Origin side 0 4 (0,4)

Solve the following systems of inequations graphically: $x - 2 y \leq 2, x + y \geq 3, - 2 x + y \leq 4, x \geq 0, y \geq 0$