Exploring Systems of Inequalities

What is a solution for a system of inequalities?

• A set of values that satisfies at least one inequality

• A mathematical expression combining inequalities

• An ordered pair that satisfies each inequality in the system

• A graphical representation of inequalities

What method is used to start graphing the inequality y > x^2?

• Plotting the inequality directly

• Using a solid line to represent the boundary

• Shading outside the parabola

• Pretending the inequality is an equality

Why do we use a dotted line when graphing y > x^2?

• The inequality includes the equal sign

• It represents a weak inequality

• It indicates that the boundary is not included in the solution

• To differentiate from other graphs

What is the correct test point used to determine the shading for the inequality y > x^2?

• (1, 0)

• (1, 1)

• (0, 1)

• (0, 0)

How do you isolate y in the inequality 2x + 3y < 4?

• Add 2x to both sides

• Divide all terms by 3

• Subtract 2x from both sides and then divide by 3

• Multiply all terms by 2

What is the slope and y-intercept of the line represented by the equation y = -2/3x + 4/3?

• Slope: -3/2, y-intercept: 3/4

• Slope: 2/3, y-intercept: -4/3

• Slope: 3/2, y-intercept: 3/4

• Slope: -2/3, y-intercept: 4/3

Which quadrant do the inequalities x >= 0 and y >= 0 primarily concern?

• Fourth quadrant

• First quadrant

• Third quadrant

• Second quadrant

What is the y-intercept of the line y = -2x + 10?

• -2

• 2

• -10

• 10

Which point is used as a test point for the inequality y <= -2x + 10?

• (-1, -1)

• (10, 10)

• (1, 1)

• (0, 0)

What is the final solution set for the system of inequalities discussed?

• The area below the blue line

• The intersection of all shaded areas

• The area above the red line

• The region shaded in bright pink