Writing Systems of Equations from 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 the perimeter of a rectangle?

Back

The perimeter P of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width.

Front

What does it mean when the length of a rectangle is described as '4 meters less than 3 times the width'?

Back

This means that the length l can be expressed as l = 3w - 4, where w is the width.

Front

How do you write an equation for the total cost of items purchased?

Back

If t is the price of one item and n is the number of items, the total cost C can be expressed as C = tn.

Front

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

Back

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

Front

How do you set up a system of equations from a word problem?

Back

Identify the relationships between the variables based on the information given in the problem and write equations that represent those relationships.

Front

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

Back

Coefficients represent the relationship between the variables. For example, in the equation 6t + 8g = 50, 6 and 8 indicate how many of each item is being purchased.

Front

What does it mean if two equations in a system are dependent?

Back

Dependent equations are those that represent the same line, meaning they have infinitely many solutions.

Front

What does it mean if two equations in a system are independent?

Back

Independent equations are those that represent different lines, meaning they have exactly one solution.

Front

What is the solution to a system of equations graphically?

Back

The solution is the point where the graphs of the equations intersect.