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 for a system of equations to have one solution?

Back

The lines intersect at exactly one point, representing a unique solution.

Front

What does it mean for a system of equations to have no solution?

Back

The lines are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

The lines coincide, meaning they are the same line.

Front

How do you graph a linear equation?

Back

You can plot points that satisfy the equation and connect them to form a line.

Front

What is the slope of a line?

Back

The slope is the ratio of the rise (change in y) to the run (change in x).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis.

Front

How can you determine the solution of a system of equations graphically?

Back

By finding the point where the lines intersect on the graph.

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are constants.

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.