Word Problems - Systems and Otherwise

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations in the system.

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 reflect the problem's constraints.

Front

What does it mean if two equations are dependent?

Back

Dependent equations have infinitely many solutions, meaning they represent the same line in a graph.

Front

What does it mean if two equations are independent?

Back

Independent equations have exactly one solution, meaning they intersect at a single point in a graph.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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.

Front

How do you find the perimeter of a rectangle?

Back

The perimeter P of a rectangle is calculated using the formula P = 2(length + width).

Front

What is the relationship between the length and width of a rectangle if the length is twice the width?

Back

If the length L is twice the width W, then L = 2W.

Front

How do you set up an equation for a total cost problem involving fixed and variable costs?

Back

The total cost equation is typically in the form: Total Cost = Fixed Cost + (Variable Cost per unit * Number of units).

Front

What is the first step in solving a word problem involving money and bills?

Back

Define variables for each type of bill and set up equations based on the total number of bills and the total amount of money.