FLASHCARD: Linear Systems of Equation (11.1, 11.2, and 11.3)

Front

What is a linear system of equations?

Back

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

Front

What does it mean if a system has no solutions?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system has one solution?

Back

The lines intersect at exactly one point.

Front

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

Back

The lines coincide, meaning they are the same line.

Front

How do you find the y-intercept of a linear equation?

Back

Set x = 0 in the equation and solve for y.

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) between two points on the line.

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

How can you determine if two lines are parallel?

Back

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

Front

How can you determine if two lines are perpendicular?

Back

If the product of their slopes is -1.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.