Week #13 System of Equations Word Problems

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that can be solved together.

Front

What does it mean for a system of equations to have one solution?

Back

The lines representing the equations intersect at exactly one point.

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 does it mean for a system of equations to have infinitely many solutions?

Back

The lines representing the equations coincide, meaning they are the same line.

Front

How do you represent a word problem as a system of equations?

Back

Identify variables for the unknowns, translate the problem into equations based on relationships described.

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.

Front

What is the elimination method in solving systems of equations?

Back

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

Front

How can you check the solution of a system of equations?

Back

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

Front

What is the graphical method of solving systems of equations?

Back

Graph both equations on the same coordinate plane and identify the point(s) of intersection.

Front

What is a linear equation?

Back

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