Determine the Number of Solutions for Equations

Front

What does it mean when two equations have no solution?

Back

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

Front

What does it mean when two equations have one solution?

Back

It means that the lines represented by the equations intersect at exactly one point.

Front

What does it mean when two equations have infinitely many solutions?

Back

It means that the lines represented by the equations are the same line, overlapping completely.

Front

Given the equations y = 2x + 5 and y = 2x - 3, how many solutions are there?

Back

No solution.

Front

Given the equations y = 3x + 2 and y = -3x + 2, how many solutions are there?

Back

1 solution.

Front

Given the equations y = -x + 2 and y = -x + 2, how many solutions are there?

Back

Infinitely many solutions.

Front

Given the equations y = 5x - 2 and y = 2x - 5, how many solutions are there?

Back

1 solution.

Front

Given the equations y = -7x + 2 and 2y = -14x + 6, how many solutions are there?

Back

No solution.

Front

What is the graphical representation of two equations with no solution?

Back

Two parallel lines on a graph.

Front

What is the graphical representation of two equations with one solution?

Back

Two lines that intersect at a single point on a graph.