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 two lines to intersect?

Back

It means they have one solution, which is the point where they cross.

Front

What are parallel lines?

Back

Lines that never intersect and have the same slope.

Front

What type of lines have no solution when graphed?

Back

Parallel lines.

Front

What are coinciding lines?

Back

Lines that lie on top of one another, representing infinitely many solutions.

Front

How do you solve a system of equations by graphing?

Back

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

Front

What does the point of intersection represent in a system of equations?

Back

It represents the solution to the system, where both equations are true.

Front

What is the slope-intercept form of a line?

Back

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

Front

How can you determine if a system has one solution, no solution, or infinitely many solutions?

Back

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

Front

What is the y-intercept of the equation y = -x + 5?

Back

5, which is the point where the line crosses the y-axis.