Systems of Linear Equations (with special cases)

Front

What does it mean if a system of equations has no solution?

Back

It means that the lines represented by the equations are parallel and will never intersect.

Front

What does the graph of a system with infinitely many solutions look like?

Back

The graph consists of the same line represented by both equations, meaning they overlap completely.

Front

How can you determine if a system of equations has one solution?

Back

If the lines intersect at exactly one point, the system has one solution.

Front

What are the possible types of solutions for a system of linear equations?

Back

0 solutions (parallel lines), 1 solution (intersecting lines), or infinitely many solutions (same line).

Front

If two lines are skew, what does that imply about their solutions?

Back

Skew lines do not intersect and are not parallel, meaning the system has no solution.

Front

What is the solution to the system represented by the point (0, 2)?

Back

The solution is the point where the two lines intersect, which is (0, 2).

Front

What does it mean if a system of equations has exactly two solutions?

Back

A system of linear equations cannot have exactly two solutions; it can have none, one, or infinitely many.

Front

How do you graph a system of equations to find the solution?

Back

You plot both equations on the same graph and look for the point(s) where they intersect.

Front

What is the significance of the slopes of two lines in a system of equations?

Back

If the slopes are equal and the y-intercepts are different, the lines are parallel (no solution). If the slopes are different, the lines intersect (one solution).

Front

What is the definition of a linear equation?

Back