Chapter 6 Review-System of Equations and Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables. Solutions are the values that satisfy all inequalities in the system.

Front

What does it mean if a system of linear equations has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of linear equations has infinitely many solutions?

Back

The lines represented by the equations are the same line, meaning every point on the line is a solution.

Front

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

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the graphical representation of a linear inequality?

Back

A shaded region on one side of the line, indicating all the solutions that satisfy the inequality.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means the value is greater than, not including the boundary. '≥' means the value is greater than or equal to, including the boundary.

Front

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

Back

It is often represented as a shaded area on a graph, showing all possible solutions.

Front

How can you tell if two lines are intersecting?

Back

If the lines have different slopes, they will intersect at one point.

Front

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

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, indicating the value of y when x = 0.