Solve Systems by Inspection

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have no solution?

Back

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

Front

What does it mean for a system of equations to have one solution?

Back

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

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

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

Front

How can you determine if two equations have no solution by inspection?

Back

If the slopes are the same but the y-intercepts are different, the system has no solution.

Front

How can you determine if two equations have one solution by inspection?

Back

If the slopes are different, the system has one solution.

Front

How can you determine if two equations have infinitely many solutions by inspection?

Back

If both the slope and y-intercept are the same, the system has infinitely many solutions.

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

Given the equations y = 2x - 11 and y = 2x + 5, how many solutions does this system have?

Back

None.

Front

Given the equations y = ¾x + 5 and y = ¾x + 2, how many solutions does this system have?

Back

No Solution.