Question

four times a number added to 3 times a larger number is 31. seven subtracted from the larger number is equal to twice the smaller number. let x represent the smaller number and y represent the larger number. which equations represent this situation?

\\( y = -\frac{4}{3}x + 31 \\)
\\( y = 2x + 7 \\)

\\( y = -\frac{4}{3}x + \frac{31}{3} \\)
\\( y = 2x + 7 \\)

\\( y = -\frac{4}{3}x + 31 \\)
\\( y = -2x + 7 \\)

\\( y = -\frac{4}{3}x + \frac{31}{3} \\)
\\( y = -2x + 7 \\)

Explanation:

Identify variables

Using the Variable Identification knowledge point

$$
LATEXBLOCK0
$$

Translate first statement

Using the Algebraic Translation knowledge point

$$
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Translate second statement

Using the System of Equations Translation knowledge point

$$
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$$

Match with options

Using the Slope-Intercept Form knowledge point

$$
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$$

Answer:

• (A) \(y = -\frac{4}{3}x + 31\) and \(y = 2x + 7\)
• (B) \(y = -\frac{4}{3}x + \frac{31}{3}\) and \(y = 2x + 7\) (Correct answer)
• (C) \(y = -\frac{4}{3}x + 31\) and \(y = -2x + 7\)
• (D) \(y = -\frac{4}{3}x + \frac{31}{3}\) and \(y = -2x + 7\)