Systems - Number of Solutions

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 one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations coincide, meaning they are the same line.

Front

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

Back

By analyzing the slopes and y-intercepts of the equations.

Front

What is the slope of the line represented by the equation y = mx + b?

Back

The slope is 'm', which indicates the steepness and direction of the line.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept is 'b', the point where the line crosses the y-axis.

Front

If two lines have the same slope but different y-intercepts, how many solutions does their system have?

Back

No solution, as the lines are parallel.

Front

If two lines have different slopes, how many solutions does their system have?

Back

One solution, as the lines intersect at a single point.

Front

What is the solution to a system of equations?

Back

The point(s) (x, y) that satisfy all equations in the system.