Graphing 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 lines representing the equations are parallel and never intersect.

Front

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

Back

By observing the intersection points of the lines; no intersection means no solution, one intersection means one solution, and infinite intersections mean infinitely many solutions.

Front

What does it mean if two lines intersect at a single point?

Back

The system of equations has exactly one solution.

Front

What is the graphical representation of the equation y = mx + b?

Back

A straight line where m is the slope and b is the y-intercept.

Front

How do you find the solution to a system of equations graphically?

Back

By plotting both equations on the same graph and identifying the point(s) where they intersect.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it moves (positive or negative).

Front

What does it mean if two lines are coincident?

Back

They lie on top of each other, representing infinitely many solutions.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How can you solve a system of equations algebraically?

Back

By using methods such as substitution, elimination, or matrix operations.