24-25 - Flashcard - Graphing Systems of Eq and 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 region where the graphs of the inequalities overlap.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the region that satisfies the inequality.

Front

What does the solution to a system of equations represent?

Back

The solution to a system of equations represents the point(s) where the graphs of the equations intersect.

Front

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

Back

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

Front

How do you find the intersection of two lines given by equations?

Back

To find the intersection, solve the system of equations simultaneously, either by substitution or elimination, to find the point (x, y) where they meet.

Front

What is the graphical representation of the inequality y > 2x - 4?

Back

Graph the line y = 2x - 4 with a dashed line and shade the region above the line.

Front

What does it mean if a point lies in the solution region of a system of inequalities?

Back

If a point lies in the solution region, it satisfies all inequalities in the system.

Front

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

Back

Substitute the point's coordinates into each equation. If the equations hold true, the point is a solution.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes. A positive slope means the line rises, while a negative slope means it falls.

Front

What is the y-intercept in the equation of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.