Applications of Systems

Front

What does the graph of a system of equations with no solution look like?

Back

The graph consists of parallel lines.

Front

Write a system of equations for Caitlin's money problem where T = # of $20 bills and F = # of $50 bills.

Back

T + F = 49 and 20T + 50F = 1430.

Front

In a pasture with horses and chickens, if there are 28 animals and 80 legs, how can we represent this situation with equations?

Back

Let H = number of horses and C = number of chickens. The system is: H + C = 28 and 4H + 2C = 80.

Front

If Erin is 3 years younger than twice Alex's age and their ages combined are 33, how can we express this as a system of equations?

Back

Let x = Erin's age and y = Alex's age. The system is: x + y = 33 and x = 2y - 3.

Front

Christian ordered brochures costing a total of $134 for 4 boxes of black-and-white and 3 boxes of color. How can we represent this situation with equations?

Back

Let x = cost of black-and-white brochures and y = cost of color brochures. The system is: 4x + 3y = 134.

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 be consistent?

Back

A consistent system has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions.

Front

What is the graphical representation of a consistent system with exactly one solution?

Back

The graph shows two intersecting lines.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.