Systems Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean if a system has no solution?

Back

It means the lines representing the equations are parallel and never intersect.

Front

What does it mean if a system has one solution?

Back

It means the lines representing the equations intersect at exactly one point.

Front

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

Back

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

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 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

How do you determine if a system is consistent or inconsistent?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

What is the graphical representation of a system of equations?

Back

It is the visual depiction of the equations on a coordinate plane, showing the lines and their intersections.

Front

What is the first step in solving a system of equations by elimination?

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

What does it mean to graph an equation?

Back

To plot all the points that satisfy the equation on a coordinate plane.