Solving Systems

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 no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

How can you determine if a system of equations has a unique solution?

Back

If the lines represented by the equations intersect at exactly one point, the system has a unique solution.

Front

What is the graphical representation of a system of equations with no solution?

Back

Two parallel lines that do not intersect.

Front

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

Back

Two overlapping lines that represent the same equation.

Front

What is the first step in using the elimination method?

Back

Align the equations so that corresponding variables are in the same column.

Front

How do you know if two equations are dependent?

Back

If one equation can be obtained by multiplying or dividing the other by a non-zero constant.

Front

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

Back

A single point where the graphs of the equations intersect.