Flashcard 13.1-13.3. Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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 elimination?

Back

You add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of a system of equations?

Back

The solution is where the graphs of the equations intersect.

Front

What is the solution to the system: 2x + 3y = 6 and 4x + 6y = 12?

Back

Infinitely many solutions.

Front

What is the solution to the system: x + y = 5 and x - y = 1?

Back

(3, 2).

Front

What does it mean if two equations are dependent?

Back

They represent the same line and have infinitely many solutions.

Front

What does it mean if two equations are independent?

Back

They represent different lines and have exactly one solution.

Front

What is the substitution method in solving systems of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.