Systems of Equations Word Problems

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 'd' and 'n' represent in the context of coin problems?

Back

In coin problems, 'd' typically represents the number of dimes and 'n' represents the number of nickels.

Front

What is the significance of the total number of coins in a coin problem?

Back

The total number of coins provides one equation in the system, helping to relate the quantities of different types of coins.

Front

How do you set up an equation for total value in a coin problem?

Back

Multiply the number of each type of coin by its value and set the sum equal to the total value given in the problem.

Front

What does 'x' and 'y' represent in age-related word problems?

Back

In age-related problems, 'x' often represents one person's age and 'y' represents another person's age.

Front

How do you express relationships between ages in equations?

Back

Use expressions that relate the ages, such as 'x = y - 3' or 'y = 2x' to represent age differences or ratios.

Front

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

Back

The first step is to write the equations in a standard form, ensuring all variables are on one side and constants on the other.

Front

What is substitution in the context of solving systems of equations?

Back

Substitution involves solving one equation for a variable and then substituting that expression into the other equation.

Front

What is elimination in the context of solving systems of equations?

Back

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