Solving Systems of Equations

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 two equations represent the same line when graphed?

Back

It means there are infinite solutions to the system.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines represent the solutions.

Front

What is a unique solution in the context of systems of equations?

Back

A unique solution occurs when the lines intersect at exactly one point.

Front

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

Back

Parallel lines indicate that there is no solution to the system.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, often represented by parallel lines.

Front

What does it mean for a system of equations to be dependent?

Back

A dependent system has infinitely many solutions, represented by the same line.