Linear Inequalities in Two Variables

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Which of the following represents a linear inequality in two variables?

$4x - 5y \geq 12$

What is the solution set for the inequality $-2x + 5y > 10$?

$(x, y) | x \geq -2, y \geq 3$

Which of the following inequalities represents a line with a shaded region below it on the coordinate plane?

$2x - 3y \leq 6$

For the inequality $3x - 4y \geq 12$, which quadrant(s) would contain the solution set?

<p>Quadrants I and IV</p> Signup and view all the answers

What is a linear inequality in two variables?

<p>An inequality in the form of Ax + By &lt; C or Ax + By &gt; C, where A, B, and C are constants and x and y are variables.</p> Signup and view all the answers

How is the solution set for a linear inequality in two variables represented on the coordinate plane?

<p>The solution set is represented by shading the region of the plane that satisfies the inequality.</p> Signup and view all the answers

What does it mean for a point to be in the solution set of a linear inequality in two variables?

<p>If a point satisfies the inequality when its coordinates are substituted into the inequality, then it is in the solution set.</p> Signup and view all the answers

What are the possible orientations of the boundary line in a linear inequality in two variables?

<p>The boundary line can be horizontal, vertical, or slanted, depending on the coefficients of x and y in the inequality.</p> Signup and view all the answers

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