Solutions to Systems of Inequalities- Graphs!

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 ordered pairs that satisfy all inequalities in the system.

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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. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the appropriate region for each inequality, and the solution 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, meaning it lies in the shaded region of the graph.

Front

How can you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≤ or ≥), while a dashed line indicates that the points on the line are not included ( < or >).

Front

What does the inequality y < -x - 1 represent graphically?

Back

The inequality y < -x - 1 represents the region below the line y = -x - 1, which has a slope of -1 and a y-intercept of -1.

Front

What is the significance of the y-intercept in graphing inequalities?

Back

The y-intercept is the point where the line crosses the y-axis. It helps in graphing the line and determining the region to shade for the inequality.

Front

How do you find the intersection of two inequalities?

Back

To find the intersection of two inequalities, graph both inequalities and identify the region where the shaded areas overlap. This overlapping region represents the solution set.

Front

What does the solution set of a system of inequalities look like?

Back

The solution set of a system of inequalities is typically a shaded region on a graph, which may be bounded or unbounded, depending on the inequalities.

Front

What is an ordered pair in the context of inequalities?

Back

An ordered pair is a pair of numbers (x, y) that represents a point on the Cartesian plane, where x is the horizontal coordinate and y is the vertical coordinate.