Solving Systems of Equations

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 for a system of equations to have one solution?

Back

It means the lines intersect at exactly one point, representing a unique solution for the variables.

Front

What does it mean for a system of equations to have no solution?

Back

It means the lines are parallel and never intersect, indicating that there is no set of values that satisfies both equations.

Front

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

Back

It means the equations represent the same line, so there are countless points that satisfy both equations.

Front

What is the substitution method 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 where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

How do you determine if two lines are identical?

Back

Two lines are identical if they have the same slope and the same y-intercept.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the graphs of the equations on a coordinate plane, showing their intersections.

Front

What is the first step in solving a system of equations using substitution?

Back

Isolate one variable in one of the equations.