Solving Systems

Front

What is a system of equations?

Back

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

Front

How can you determine if a point is a solution to a system of equations?

Back

The (x,y) coordinates must satisfy all equations in the system.

Front

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

Back

The lines represented by the equations are parallel and do not intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines represent the solutions to the system.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

They have the same slope but different y-intercepts, resulting in no points of intersection.

Front

How can you identify if a system has one solution?

Back

The lines intersect at exactly one point, indicating a unique solution.

Front

What is the significance of the coefficients in a system of equations?

Back

They determine the slope and position of the lines in the graph.