Systems 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 point(s) where the equations intersect.

Front

How do you represent a word problem as an equation?

Back

Identify the variables, translate the problem into mathematical expressions, and set up an equation based on the relationships described.

Front

What does it mean to solve a system of equations?

Back

To find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the intersection of two lines?

Back

Set the equations equal to each other and solve for the variable. The solution gives the coordinates of the intersection point.

Front

What is a variable in mathematics?

Back

A variable is a symbol used to represent an unknown value in mathematical expressions or equations.

Front

What is the purpose of using a setup fee in a word problem?

Back

A setup fee is a fixed cost that must be added to the total cost, regardless of the number of items purchased.

Front

How do you express a total cost in a word problem?

Back

Total cost can be expressed as the sum of fixed costs and variable costs, often represented as C = mx + b, where m is the cost per item, x is the number of items, and b is the fixed cost.

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients represent the rate of change of the dependent variable with respect to the independent variable.

Front

How do you set up an equation from a word problem involving two quantities?

Back

Define variables for each quantity, write equations based on the relationships described, and include any constraints or totals given.