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 lines have a common solution, which is the point where they meet.

Front

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

Back

Graph both equations on the same coordinate plane and identify the point of intersection.

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 slope-intercept form of a linear equation?

Back

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

Front

What does it mean if two lines are parallel?

Back

They have the same slope and will never intersect, meaning there is no solution to the system.

Front

What does it mean if two lines are coincident?

Back

They lie on top of each other, meaning there are infinitely many solutions to the system.

Front

How can you determine the slope from two points?

Back

Use the formula (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The y-coordinate where the line crosses the y-axis (x=0).

Front

What is the x-intercept of a line?

Back

The x-coordinate where the line crosses the x-axis (y=0).