Systems: Number of Solutions

Front

What is a system of linear equations?

Back

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

Front

What does it mean if two lines in a graph are parallel?

Back

They have the same slope but different y-intercepts, meaning they will never intersect.

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

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

Back

The lines intersect at exactly one point.

Front

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

Back

The equations represent the same line, meaning they overlap completely.

Front

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

Back

Two parallel lines that never intersect.

Front

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

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the slope of a line?

Back

The rate at which the line rises or falls, calculated as the change in y over the change in x.

Front

What happens to the solution of a system if the lines are the same?

Back

There are infinitely many solutions since every point on the line is a solution.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, indicating the value of y when x is zero.