Graphing Systems of Linear Equations

Front

What is a system of linear equations?

Back

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

Front

What does it mean to graph a linear equation?

Back

To plot all the points that satisfy the equation on a coordinate plane.

Front

What is the solution to a system of linear equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What does it mean if a system of linear equations has no solution?

Back

The lines are parallel and never intersect.

Front

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

Back

The lines are the same, meaning they overlap completely.

Front

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

Back

By plotting the equations on a graph and identifying the intersection point.

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 slope in a linear equation?

Back

It represents the rate of change of y with respect to x.

Front

What is the y-intercept of a linear equation?

Back

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

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.