Question

twice a number added to a smaller number is 5. the difference of 5 times the smaller number and the larger number is 3. let x represent the smaller number and y represent the larger number. which equations represent the situation?

\\(2y + x = 5\\)
\\(5x - y = 3\\)

\\(2x + y = 5\\)
\\(5y - x = 3\\)

\\(2y + x = 5\\)
\\(y - 5x = 3\\)

\\(2x + y = 5\\)
\\(x - 5y = 3\\)

Explanation:

Identify the variables

Using the Variable Identification knowledge point

$$
LATEXBLOCK0
$$

Translate the first statement

Using the Algebraic Translation knowledge point

$$
LATEXBLOCK1
$$

Translate the second statement

Using the System of Equations Translation knowledge point

$$
LATEXBLOCK2
$$

Match with the options

Using the System of Equations knowledge point

$$
LATEXBLOCK3
$$

Answer:

• **(A) \(2y + x = 5\)

\(5x - y = 3\) (Correct answer)**

• (B) \(2x + y = 5\)

\(5y - x = 3\)

• (C) \(2y + x = 5\)

\(y - 5x = 3\)

• (D) \(2x + y = 5\)

\(x - 5y = 3\)