Solving Systems of Equations with 3 variables

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 to solve a system of equations?

Back

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

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the graphs of the equations represent the solutions.

Front

What are the possible outcomes when solving a system of equations?

Back

1. One unique solution (intersecting lines) 2. No solution (parallel lines) 3. Infinitely many solutions (coincident lines)

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

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

Back

The equations represent the same line, meaning any point on the line is a solution.

Front

What is the substitution method for solving systems of equations?

Back

Solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable, making it easier to solve for the others.

Front

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

Back

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

Front

What is a consistent system of equations?

Back

A system that has at least one solution.