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 for a system of equations to have one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What is the graphical representation of a system with infinitely many solutions?

Back

The lines are coincident, meaning they lie on top of each other.

Front

What does it mean for a system of equations to have no solution?

Back

The lines representing the equations are parallel and do not intersect.

Front

How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

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

Front

What is the slope of a line in the context of a linear equation?

Back

The slope is the ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

What is the y-intercept of a linear equation?

Back

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

Front

What is the significance of parallel lines in a system of equations?

Back

Parallel lines indicate that the system has no solution because they never intersect.

Front

What is the significance of coincident lines in a system of equations?

Back

Coincident lines indicate that the system has infinitely many solutions because they overlap completely.

Front

How can you solve a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) of intersection.