Solving Systems of Equations- all methods

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 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 lines representing the equations are the same line, meaning they intersect at every point.

Front

What is the elimination method for solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the substitution method for 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

How do you determine if two lines are parallel from their equations?

Back

If the slopes of the lines are equal and the y-intercepts are different, the lines are parallel.

Front

What is the graphical representation of a system of equations with one solution?

Back

Two lines that intersect at exactly one point.

Front

How can you represent a system of equations algebraically?

Back

By writing two or more equations that relate the same variables.

Front

What is the purpose of finding the intersection of two lines in a system of equations?

Back

To find the values of the variables that satisfy both equations simultaneously.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.