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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