number of solutions to a system of equations

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 no solution?

Back

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

Front

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

Back

It means the lines intersect at exactly one point.

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

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

Back

By graphing the equations and observing the points of intersection.

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, there are no solutions. If the slopes are different, there is one solution. If the slopes and y-intercepts are the same, there are 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

If two equations are identical, how many solutions does the system have?

Back

Infinitely many solutions.

Front

What is the graphical representation of the equations y = 3x - 1 and y = 3x - 1?

Back

They represent the same line, indicating infinitely many solutions.

Front

What is the graphical representation of the equations y = 4x + 2 and y = 4x + 2.01?

Back

They are parallel lines, indicating no solutions.