Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the region that satisfies the inequality. The solution to the system is where the shaded regions overlap.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system when substituted into them.

Front

What is the difference between a solution to an inequality and a solution to an equation?

Back

A solution to an inequality is a range of values that make the inequality true, while a solution to an equation is a specific value that makes the equation true.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you determine if a point is a solution to a given inequality?

Back

To determine if a point is a solution to an inequality, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a graph to represent a function?

Back

A graph represents a function if every vertical line intersects the graph at most once, which is known as the vertical line test.

Front

What is a boundary line in the context of inequalities?

Back

A boundary line is the line that represents the equation of the inequality. It divides the coordinate plane into two half-planes.

Front

How do you find the solution set of a system of inequalities?

Back

To find the solution set of a system of inequalities, graph each inequality, shade the appropriate regions, and identify the overlapping shaded area.