Solving Systems by Graphing and qualitative graphs

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations by graphing?

Back

It means to graph each equation on the same coordinate plane and find the point(s) where they intersect.

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

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 coincide in a system of equations?

Back

It means there are infinitely many solutions, as the lines overlap completely.

Front

What is a qualitative graph?

Back

A graph that shows the general shape and trend of data without precise numerical values.

Front

What does a horizontal line represent in a distance-time graph?

Back

It represents a situation where the object is at rest, with no change in distance over time.

Front

What does a vertical line represent in a distance-time graph?

Back

It is not possible in a distance-time graph, as it would imply an infinite speed.

Front

What does a slope of zero indicate in a graph?

Back

It indicates that there is no change in the dependent variable as the independent variable changes.

Front

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

Back

By substituting the point's coordinates into each equation to see if they hold true.