Application of Systems

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 equations represent parallel lines that never intersect.

Front

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

Back

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

Front

How do you solve a system of equations by graphing?

Back

You graph each equation on the same coordinate plane and identify the point(s) where they intersect.

Front

What is the substitution method in solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

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

Back

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

Front

How can you represent a real-world situation as a system of equations?

Back

By defining variables for the quantities involved and writing equations based on the relationships between them.

Front

What is the graphical representation of the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What does it mean if two equations in a system are dependent?

Back

It means they represent the same line and have infinitely many solutions.