5C Solving Systems

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved simultaneously.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What are the three main methods for solving systems of equations?

Back

1. Graphing 2. Substitution 3. Elimination

Front

What is the substitution method?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method?

Back

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

Front

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

Back

The lines represented by 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, meaning every point on the line is a solution.

Front

How can you determine if a system of equations is consistent or inconsistent?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

What is a linear equation?

Back

An equation that forms a straight line when graphed, typically in the form y = mx + b.

Front

What is the graphical method for solving systems of equations?

Back

Plotting the equations on a graph and identifying the point(s) where they intersect.