Homework: 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 can be solved together.

Front

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

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are the same line, meaning they intersect at every point.

Front

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

Back

Identify the variables, translate the relationships into equations, and set them equal to each other.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other.

Front

What is the first step in solving a system of equations by elimination?

Back

Align the equations and manipulate them to eliminate one variable.

Front

In the equation 10c + 5d = 16.50, what do c and d represent?

Back

c represents the cost of coffee and d represents the cost of doughnuts.

Front

How can you check if your solution to a system of equations is correct?

Back

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

Front

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

Back

Coefficients represent the rate of change or the quantity of each variable in the equations.