Systems of Equations Word Problems

Front

What does the graph of a system of equations with infinitely many solutions look like?

Back

The same line.

Front

What is the system of equations for the problem: Carla purchased a math textbook and a novel for a total of $54, with the textbook costing $8 more than 3 times the price of the novel?

Back

t + n = 54 and t = 3n + 8.

Front

What equations represent the system for the ticket sales problem where 3 senior citizen tickets and 1 child ticket sold for $38, and 3 senior citizen tickets and 2 child tickets sold for $52?

Back

3s + 1c = 38 and 3s + 2c = 52.

Front

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

Back

The lines are parallel and never intersect.

Front

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

Back

The lines are the same line, overlapping each other.

Front

What is a system of equations?

Back

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

Front

How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and 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.

Front

What does it mean for two lines to be skew?

Back

They are non-parallel lines that do not intersect and are not in the same plane.