Flashcard 6: 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 no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of linear equations has one solution?

Back

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

Front

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

Back

The lines represented by the equations are the same line, overlapping each other.

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 standard form of a linear equation?

Back

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

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the constant of variation in direct variation?

Back

The constant ratio k in the equation y = kx.

Front

If y varies directly with x and y = 7 when x = 14, what is the constant of variation?

Back

k = 1/2.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.