Solving Systems of Equations by Graphing

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never intersect. They have the same slope.

Front

What does it mean for two lines to intersect?

Back

Two lines intersect when they cross each other at a point, which represents a solution to the system of equations.

Front

How can you determine if a system of equations has no solution?

Back

A system of equations has no solution if the lines are parallel, meaning they have the same slope but different y-intercepts.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

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

Back

To find the solution, graph both equations on the same coordinate plane and identify the point where they intersect.

Front

What does it mean if two lines have the same slope?

Back

If two lines have the same slope, they are parallel and will never intersect, indicating no solution for the system.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

How can you identify the coordinates of an intersection point?

Back

The coordinates of an intersection point can be identified by the values of x and y at the point where the two lines meet.

Front

What is the significance of the solution to a system of equations?

Back

The solution represents the values of the variables that satisfy both equations simultaneously.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the two equations represent the same line, meaning they overlap completely.