Solving Systems of Equations 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 two lines to intersect?

Back

It means that the two lines have a common solution, which is the point where they meet.

Front

How can you find the solution to a system of equations by graphing?

Back

By graphing both equations on the same coordinate plane and identifying the point of intersection.

Front

What is the y-intercept of a line?

Back

The y-coordinate of the point where the line crosses the y-axis.

Front

How do you determine the slope of a line from a graph?

Back

The slope is determined by the rise over run between two points on the line.

Front

What does a positive slope indicate about a line?

Back

It indicates that as x increases, y also increases.

Front

What does a negative slope indicate about a line?

Back

It indicates that as x increases, y decreases.

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 solution to a system of equations?

Back

It represents the values of the variables that satisfy all equations in the system.

Front

What does it mean if two lines are parallel?

Back

It means they have the same slope and will never intersect, indicating no solution to the system.