How Many Solutions?

Front

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

Back

No Solution, One Solution, Infinitely Many Solutions.

Front

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

Back

The equations represent parallel lines that never intersect.

Front

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

Back

The equations represent lines that intersect at exactly one point.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel and have the same slope but different y-intercepts.

Front

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

Back

If the lines have different slopes and intersect at one point.

Front

How can you determine if a system of equations has infinitely many solutions?

Back

If the equations are equivalent, meaning they represent the same line.

Front

What is the definition of infinite solutions?

Back

No matter what constant is substituted in for the variable, the equation is ALWAYS true.

Front

What is an example of a system with no solution?

Back

x + y = 2 and x + y = 5.

Front

What is an example of a system with one solution?

Back

2x + 3y = 6 and x - y = 1.