Graph Systems of Equations & Inequalities Rvw

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

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 it satisfies all equations, it is a solution.

Front

What does it mean for a system of equations to have one solution?

Back

It means that the equations represent two lines that intersect at exactly one point.

Front

What is the graphical representation of a system of inequalities?

Back

It is represented by shaded regions on a graph, indicating the area where the solutions lie.

Front

What are intersecting lines in the context of systems of equations?

Back

Lines that cross at a single point, indicating a unique solution to the system.

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 moves (positive or negative) as x changes.

Front

What does it mean for two lines to be parallel?

Back

They have the same slope but different y-intercepts, meaning they will never intersect.

Front

How do you graph a system of inequalities?

Back

Graph each inequality as if it were an equation, then shade the appropriate region based on the inequality sign.

Front

What is the difference between a consistent and inconsistent system of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.