Problem 2 - Beginning and Intermediate Algebra

Question

If \(x=2\) and \(y=1,\) then the value of \(x y\) is A. \(\frac{1}{2}\) B. 1 C. 2 D. 3

Step-by-Step Solution

Answer

The value of \( x y \) is 2.

Step 1: Understand the Problem

We need to find the value of the expression ewline \( x y \) where \( x = 2 \) and \( y = 1 \).

Step 2: Substitute the Given Values

Substitute \( x = 2 \) and \( y = 1 \) into the expression \( x y \). This gives us ewline\( 2 \times 1 \).

Step 3: Perform the Multiplication

Multiply the values: ewline \( 2 \times 1 = 2 \).

Key Concepts

Multiplication

Multiplication is a fundamental arithmetic operation. It involves finding the total of one number added repeatedly, a certain number of times. For example, multiplying 2 by 1 means taking the number 2 and not changing it, as it's only being multiplied by 1. This is represented as 2 in the final computation.
Here are some key points about multiplication:

• The numbers being multiplied are called 'factors'.
• The answer to a multiplication problem is called the 'product'.
• Multiplying any number by 1 returns the original number, e.g., 2 × 1 = 2.

In our exercise, we multiplied the given values of x and y. Substituting these, we calculated 2 × 1 which equals 2.

Substitution

Substitution in algebra means replacing variables with given numerical values. This method simplifies expressions and makes them easier to solve. In our original exercise, we used substitution to replace x and y with their specific values, 2 and 1 respectively.
To perform substitution successfully:

• Identify what each variable represents.
• Replace the variables with their given values directly into the expression.
• Solve the simplified expression as necessary.

In the exercise, after substituting x = 2 and y = 1 into the expression xy, we got 2 × 1, which was then easily calculated.

Basic Algebra

Basic algebra involves working with mathematical expressions that include variables. A variable is a symbol, often a letter, that represents a number which can change or is unknown. Algebraic operations are similar to regular arithmetic but require handling variables.
Here are a few pointers on basic algebra:

• Simplify expressions by combining like terms.
• Perform arithmetic operations such as addition, subtraction, multiplication, and division following the order of operations.
• Substitute known values to simplify the expression further.

In our problem, the expression was xy, where both variables had known values. By substituting and then multiplying, we showed that xy = 2. Basic algebra allowed us to systematically find the product of the expression.