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 two equations represent the same line?

Back

The system has infinitely many solutions.

Front

How do you determine if a system of equations has no solution?

Back

If the lines are parallel and have different slopes.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

What is the significance of the slopes of two lines in a system of equations?

Back

If the slopes are equal, the lines are parallel; if they are different, the lines will intersect.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.