Solving Systems by Graphing

Front

What is a system of equations?

Back

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

Front

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

Back

It means the lines representing the equations are parallel and never intersect.

Front

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

Back

It means the lines intersect at exactly one point.

Front

What does it mean for a system to have infinitely many solutions?

Back

It means the lines are the same, having the same slope and y-intercept.

Front

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

Back

By analyzing the slopes and y-intercepts of the lines.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis.

Front

How do you graph a linear equation?

Back

By plotting points that satisfy the equation and connecting them with a straight line.

Front

What is the graphical representation of parallel lines?

Back

Two lines that never intersect and have the same slope.

Front

What is the graphical representation of intersecting lines?

Back

Two lines that cross at a single point, indicating one solution.