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Mathematics

Algebra

Systems of Linear Inequalities

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$y \geq -3x + 4$ , $y \leq \frac{1}{4}x + 2$

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

$y < 5 - 2x$ , $y \geq -\frac{3}{4}x + 1$

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

$2y \leq -3x + 4$ , $x - y > 1$

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

$y \leq 4x - 1$ , $2y > -x + 3$

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

$3y - x \leq 9$ , $y + 3x > 6$

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

$3y + x \geq 6$ , $y - 5x < -10$

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

$4y + x \geq 8$ , $2y - 3x < -6$

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

$-2y > 4x - 6$ , $y \leq x + 4$

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

$y \leq 2x + 3$ , $y > -x + 1$

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

$4y - 3x \geq 12$ , $x + y < 5$

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

$2y - x < 4$ , $y + x \geq 2$

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

$y + 2x > 3$ , $y - x \leq -2$

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

$y \geq -2x + 5$ , $y < x - 1$

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

$y \leq -\frac{1}{2}x + 5$ , $y > 2x - 1$

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

$y < -x + 6$ , $y \leq \frac{3}{2}x$

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

$2y \geq -4x + 1$ , $3y + 2x < 6$

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

$y \leq \frac{5}{2}x - 3$ , $y \geq -x + 2$

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

$y + \frac{1}{2}x \leq 3$ , $y - 2x > 4$

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

$y \geq x - 2$ , $y < 3x + 1$

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

$y > -\frac{1}{3}x + 2$ , $y \leq 2x - 5$

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

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