Systems - Number of Solutions

Front

What is a system of equations?

Back

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

Front

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

Back

The graphs of the equations intersect at exactly one point.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

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

Back

The graphs of the equations are the same line, overlapping at all points.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the slope of a line?

Back

The steepness of the line, calculated as the rise over run (change in y over change in x).

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

If two lines have the same slope but different y-intercepts, how many solutions does the system have?

Back

No solution, because the lines are parallel.

Front

If two lines have different slopes, how many solutions does the system have?

Back

One solution, because the lines intersect at one point.

Front

If two lines are the same, how many solutions does the system have?

Back

Infinitely many solutions, because they overlap completely.