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Linear Inequalities in Two Variables

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Questions and Answers

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

$3x - 2y = 8$
$2x + 3y \< 7$
$4x - 5y \geq 12$ (correct)
$x^2 + y^2 = 9$

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

$(x, y) | x \leq -2, y \leq 3$
$(x, y) | x \geq -2, y > 3$
$(x, y) | x \geq -2, y \geq 3$ (correct)
$(x, y) | x > -2, y < 3$

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

$3x + 2y > 10$
$2x - 3y \leq 6$ (correct)
$-2x + 3y < 9$
$4x + 5y = 20$

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

Quadrants I and IV (D) Signup and view all the answers

What is a linear inequality in two variables?

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

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

The solution set is represented by shading the region of the plane that satisfies the inequality. 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?

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

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

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

Flashcards

Linear Inequality in Two Variables

An inequality in the form Ax + By < C or Ax + By > C where A, B, and C are constants, and x and y are variables.

Solution Set (Inequality)

The set of all points (x, y) that make the inequality true.