ACT Practice Test: Systems of Inequalities

The video tutorial explains how to determine the solution set for a system of inequalities involving a line and a circle. It begins by introducing the problem and the given equations. The tutorial then details how to graph and analyze the line inequality, focusing on the y-intercept and slope. Next, it covers the circle inequality, explaining how to find the center and radius. Finally, the video concludes by identifying the correct solution set based on the shaded region in the graph.

What does the shaded region in the graph represent?

• The solution set to a system of inequalities

• The area outside a circle

• The solution set to a single equation

• The area above a line

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

• 1

• 2

• 0

• -2

What does the slope of -1 indicate in the line y = -x + 2?

• The line goes down 2 units for every 1 unit it goes right

• The line goes up 2 units for every 1 unit it goes right

• The line goes down 1 unit for every 1 unit it goes right

• The line goes up 1 unit for every 1 unit it goes right

What does a dashed line represent in the context of inequalities?

• The inequality includes the line

• The inequality does not include the line

• The inequality is an equation

• The inequality is a quadratic

What is the general equation for a circle?

• x - h^2 + y - k^2 = r^2

• x - h + y - k = r

• x^2 + y^2 = r^2

• x - h^2 + y - k^2 = r

What are the coordinates of the center of the circle given by (x - 1)^2 + (y - 2)^2 = 9?

• (1, 2)

• (-1, 2)

• (2, 1)

• (-1, -2)

What is the radius of the circle given by (x - 1)^2 + (y - 2)^2 = 9?

• 1

• 2

• 4

• 3

What does the inequality (x - 1)^2 + (y - 2)^2 < 9 represent?

• The area outside the circle

• The area inside the circle

• The circumference of the circle

• The diameter of the circle

Which inequality represents the area below the line y = -x + 2?

• y > -x + 2

• y < -x + 2

• y = -x + 2

• y >= -x + 2

What is the correct system of inequalities for the shaded region?

• y < -x + 2 and (x - 1)^2 + (y - 2)^2 < 9

• y > -x + 2 and (x - 1)^2 + (y - 2)^2 > 9

• y = -x + 2 and (x - 1)^2 + (y - 2)^2 = 9

• y >= -x + 2 and (x - 1)^2 + (y - 2)^2 <= 9