Flashcard 6-3: System 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.

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 are the same, meaning they overlap completely.

Front

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

Back

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

Front

What is the graphical representation of the equation y = mx + b?

Back

A straight line with slope m and y-intercept b.

Front

What is the slope of a line?

Back

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

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

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

Front

What is the standard form of a linear equation?

Back

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