Solutions to Systems 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

The equations represent parallel lines that never intersect.

Front

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

Back

The equations represent lines that 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

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 graphical representation of parallel lines?

Back

Lines that run in the same direction and never meet.

Front

What is the graphical representation of intersecting lines?

Back

Lines that cross at one point, indicating a unique solution.

Front

What is the slope of a line?

Back

The steepness or incline of the line, calculated as the rise over run.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

If two lines have the same slope but different y-intercepts, what can be said about their solutions?

Back

They are parallel lines and have no solutions.