Systems of Equations: Test Review

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What is the graphical representation of intersecting lines in a system of equations?

Back

The lines cross at a point, indicating a unique solution.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, which is then substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the others.

Front

If a system of equations has infinitely many solutions, what does the graph look like?

Back

The lines are coincident, meaning they lie on top of each other.

Front

How do 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 the x-value of the solution for the system: x - 2y + z = -11, 3x + 2y - z = 7, -x + 2y + 4z = -9?

Back

-1

Front

What is the y-value of the solution for the system: x - 2y + z = -11, 3x + 2y - z = 7, -x + 2y + 4z = -9?

Back

2

Front

What is the z-coordinate of the solution for the system: x - 2y + z = -11, 3x + 2y - z = 7, -x + 2y + 4z = -9?

Back

-4