One Solution, No Solution, Many Solutions

Front

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

Back

The two lines represented by the equations intersect at exactly one point.

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = 2x - 3?

Back

No Solution (the lines are parallel).

Front

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

Back

If the two equations represent the same line, they have infinitely many solutions.

Front

What is the graphical representation of a system with no solutions?

Back

Two parallel lines that never intersect.

Front

What does it mean if two lines intersect at a single point?

Back

The system of equations has one unique solution.

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 system has no solutions. If the slopes are different, the system has one solution.

Front

What is the equation of a line in slope-intercept form?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Front

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

Back

The equations represent lines that are parallel and do not intersect.

Front

What is the relationship between the coefficients of a system of equations that has infinitely many solutions?

Back

The equations are multiples of each other, meaning they represent the same line.