Systems of Equations Review (for 5-3 Flashcard) with word problems

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 no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

What is the elimination method in solving systems of equations?

Back

A method where one equation is manipulated to eliminate one variable, allowing for the other variable to be solved.

Front

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

Back

Identify the variables, write equations based on the relationships described, and ensure they reflect the problem's conditions.

Front

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

Back

Solve one of the equations for one variable in terms of the other variable.

Front

What does the solution (x, y) represent in a system of equations?

Back

The point where the graphs of the equations intersect, indicating the values of the variables that satisfy both equations.

Front

How can you tell 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 the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the values of the solution back into the original equations to see if they hold true.

Front

What is the significance of the coefficients in a system of equations?

Back

They determine the slope and position of the lines represented by the equations.