Flashcard 6-6M: 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 if a system of linear equations has one solution?

Back

The two lines represented by the equations intersect at exactly one point.

Front

What is the y-intercept of a linear equation?

Back

The point where the line crosses the y-axis, represented as (0, y).

Front

What is the slope of a line?

Back

The rate at which the line rises or falls, calculated as the change in y over the change in x (rise/run).

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 two lines are the same line, 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 point of intersection.

Front

What is the zero of a function?

Back

The x-value where the function equals zero, also known as the x-intercept.

Front

How can you determine the slope from two points?

Back

Use the formula (y2 - y1) / (x2 - x1).

Front

What is the standard form of a linear equation?

Back

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