Solve the following system of inequalities gr | vedclass

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(B) Step $1$: Consider the boundary lines $x - y + 2 = 0$ and $2x + y - 5 = 0$. Step $2$: For $x - y + 2 = 0$,if $x = 0$,$y = 2$; if $y = 0$,$x = -2$.

Vedclass · Accepted Answer

The solution is the intersection of the half-planes defined by $x - y \geq -2$ and $2x + y \leq 5$.

Vedclass · Answer

(B) Step $1$: Consider the boundary lines $x - y + 2 = 0$ and $2x + y - 5 = 0$. Step $2$: For $x - y + 2 = 0$,if $x = 0$,$y = 2$; if $y = 0$,$x = -2$. The line passes through $(0, 2)$ and $(-2, 0)$. Testing $(0, 0)$,$0 - 0 + 2 \geq 0$ is true,so the region includes the origin. Step $3$: For $2x + y - 5 = 0$,if $x = 0$,$y = 5$; if $y = 0$,$x = 2.5$. The line passes through $(0, 5)$ and $(2.5, 0)$. Testing $(0, 0)$,$2(0) + 0 - 5 \leq 0$ is true,so the region includes the origin. Step $4$: The solution is the common shaded region satisfying both inequalities simultaneously.

Solve the following system of inequalities graphically: $x - y + 2 \geq 0$ and $2x + y - 5 \leq 0$.

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