WU: Writing Linear Systems Word Problems

Front

What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

Front

What are the possible outcomes when solving a system of linear equations?

Back

1. One solution (the lines intersect at one point). 2. No solution (the lines are parallel). 3. Infinitely many solutions (the lines coincide).

Front

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

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations represent the same scenario.

Front

What is the first step in solving a word problem involving a linear system?

Back

The first step is to define the variables that represent the unknown quantities in the problem.

Front

In the problem 'There are 15 animals in a barn. These animals are horses and chickens.', how do you define the variables?

Back

Let x = number of horses, y = number of chickens.

Front

What does the equation x + y = 15 represent in the context of the animal problem?

Back

It represents the total number of animals in the barn, where x is the number of horses and y is the number of chickens.

Front

In the equation 4x + 2y = 44, what does each term represent?

Back

4x represents the total number of legs from horses (4 legs each), and 2y represents the total number of legs from chickens (2 legs each).

Front

How do you derive the second equation in the animal problem?

Back

By counting the total number of legs: Horses have 4 legs and chickens have 2 legs, leading to the equation 4x + 2y = 44.