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 is the graphical representation of a system of equations with one solution?

Back

Two lines that intersect at a single point.

Front

What is the method of substitution 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 that involves adding or subtracting equations to eliminate one variable.

Front

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

Back

A system is consistent if it has at least one solution.

Front

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

Back

A system is inconsistent if it has no solutions.

Front

How can you determine if a system of equations has infinitely many solutions?

Back

If the equations represent the same line, they have infinitely many solutions.

Front

What is a 3-variable system of equations?

Back

A system that consists of three equations with three variables, typically represented as x, y, and z.

Front

What is the role of the determinant in solving systems of equations?

Back

The determinant helps determine if a unique solution exists for a system of linear equations.