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Systems of Linear Inequalities

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y≤2x+3y \leq 2x + 3, y>−x+1y > -x + 1

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Region on the graph above the line y=−x+1y = -x + 1 and below or on the line y=2x+3y = 2x + 3.

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y≥x−2y \geq x - 2, y<3x+1y < 3x + 1

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Region on the graph above or on the line y=x−2y = x - 2 and below the line y=3x+1y = 3x + 1.

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3y−x≤93y - x \leq 9, y+3x>6y + 3x > 6

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Region on the graph below or on the line 3y−x=93y - x = 9 and above the line y+3x=6y + 3x = 6.

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y≥−2x+5y \geq -2x + 5, y<x−1y < x - 1

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Region on the graph above or on the line y=−2x+5y = -2x + 5 and below the line y=x−1y = x - 1.

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y≤52x−3y \leq \frac{5}{2}x - 3, y≥−x+2y \geq -x + 2

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Region on the graph below or on the line y=52x−3y = \frac{5}{2}x - 3 and above or on the line y=−x+2y = -x + 2.

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−2y>4x−6-2y > 4x - 6, y≤x+4y \leq x + 4

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Region on the graph below the line y=x+4y = x + 4 and above the line y=−2x+3y = -2x + 3.

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4y+x≥84y + x \geq 8, 2y−3x<−62y - 3x < -6

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Region on the graph above or on the line 4y+x=84y + x = 8 and above the line 2y−3x=−62y - 3x = -6.

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y+12x≤3y + \frac{1}{2}x \leq 3, y−2x>4y - 2x > 4

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Region on the graph below or on the line y+12x=3y + \frac{1}{2}x = 3 and above the line y−2x=4y - 2x = 4.

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y<5−2xy < 5 - 2x, y≥−34x+1y \geq -\frac{3}{4}x + 1

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Region on the graph below the line y=5−2xy = 5 - 2x and above or on the line y=−34x+1y = -\frac{3}{4}x + 1.

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2y≤−3x+42y \leq -3x + 4, x−y>1x - y > 1

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Region on the graph below or on the line 2y=−3x+42y = -3x + 4 and below the line y=x−1y = x - 1.

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y>−13x+2y > -\frac{1}{3}x + 2, y≤2x−5y \leq 2x - 5

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Region on the graph above the line y=−13x+2y = -\frac{1}{3}x + 2 and below or on the line y=2x−5y = 2x - 5.

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3y+x≥63y + x \geq 6, y−5x<−10y - 5x < -10

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Region on the graph above or on the line 3y+x=63y + x = 6 and above the line y−5x=−10y - 5x = -10.

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2y−x<42y - x < 4, y+x≥2y + x \geq 2

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Region on the graph below the line 2y−x=42y - x = 4 and above or on the line y+x=2y + x = 2.

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y≤−12x+5y \leq -\frac{1}{2}x + 5, y>2x−1y > 2x - 1

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Region on the graph above the line y=2x−1y = 2x - 1 and below or on the line y=−12x+5y = -\frac{1}{2}x + 5.

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y≥−3x+4y \geq -3x + 4, y≤14x+2y \leq \frac{1}{4}x + 2

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Region on the graph above or on the line y=−3x+4y = -3x + 4 and below or on the line y=14x+2y = \frac{1}{4}x + 2.

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4y−3x≥124y - 3x \geq 12, x+y<5x + y < 5

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Region on the graph above or on the line 4y−3x=124y - 3x = 12 and below the line x+y=5x + y = 5.

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y<−x+6y < -x + 6, y≤32xy \leq \frac{3}{2}x

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Region on the graph below the line y=−x+6y = -x + 6 and below or on the line y=32xy = \frac{3}{2}x.

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y+2x>3y + 2x > 3, y−x≤−2y - x \leq -2

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Region on the graph above the line y+2x=3y + 2x = 3 and below or on the line y−x=−2y - x = -2.

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2y≥−4x+12y \geq -4x + 1, 3y+2x<63y + 2x < 6

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Region on the graph above or on the line 2y=−4x+12y = -4x + 1 and below the line 3y+2x=63y + 2x = 6.

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y≤4x−1y \leq 4x - 1, 2y>−x+32y > -x + 3

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Region on the graph below or on the line y=4x−1y = 4x - 1 and above the line y=−12x+32y = -\frac{1}{2}x + \frac{3}{2}.

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