Systems of Equations Word Problems

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

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has one solution?

Back

It means the lines represented by the equations intersect at exactly one point.

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

What is the substitution method?

Back

A method for solving systems of equations 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 for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

What is the graphing method?

Back

A method for solving systems of equations by graphing the equations on the same coordinate plane and identifying the point(s) of intersection.

Front

How do you determine if two equations are equivalent?

Back

Two equations are equivalent if they have the same solution set, meaning they represent the same line.

Front

What is the importance of the coefficients in a system of equations?

Back

The coefficients determine the slope and position of the lines represented by the equations.

Front

How can you tell if a system of equations is inconsistent?

Back

A system is inconsistent if it has no solutions, typically indicated by parallel lines.