Graphing Systems of Inequalities and Equations

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 if two lines are parallel in a system of equations?

Back

It means there is no solution to the system, as the lines never intersect.

Front

What does it mean if two lines are coincident in a system of equations?

Back

It means there are infinitely many solutions, as the lines lie on top of each other.

Front

How can you determine the number of solutions in a system of linear equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the graphical representation of a system of inequalities?

Back

It is represented by shaded regions on a graph, indicating the solution set.

Front

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

Back

It means the shaded regions do not overlap, indicating no common solution.

Front

What is the significance of the intersection point of two lines in a system of equations?

Back

The intersection point represents the unique solution to the system of equations.

Front

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

Back

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

Front

How do you graph a linear inequality?

Back

Graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region.

Front

What does it mean if a system of equations has exactly one solution?

Back

It means the lines intersect at a single point.