6-3 Entry Ticket

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 to solve a system of equations by elimination?

Back

It means to eliminate one variable by adding or subtracting the equations, allowing you to solve for the other variable.

Front

What is an infinite number of solutions in a system of equations?

Back

This occurs when the equations represent the same line, meaning any point on the line is a solution.

Front

What is a unique solution in a system of equations?

Back

This occurs when the equations intersect at exactly one point, providing one specific solution.

Front

What is no solution in a system of equations?

Back

This occurs when the equations represent parallel lines that never intersect.

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships into equations, and ensure they reflect the problem's conditions.

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 is the purpose of substitution in solving systems of equations?

Back

To replace one variable with an expression from another equation, simplifying the system to one equation.

Front

How can you check the solution of a system of equations?

Back

Substitute the solution back into the original equations to verify that both equations are satisfied.

Front

What does it mean for two equations to be dependent?

Back

It means they represent the same line, resulting in an infinite number of solutions.