Question

which system of equations could be graphed to solve the equation below?

\\(\log(2x+1) = 3x-2\\)

\\(y_1 = 3x, y_2 = 2x\\)

\\(y_1 = \log(2x+1), y_2 = 3x-2\\)

\\(y_1 = \log 2x+1, y_2 = 3x-2\\)

\\(y_1 = \log(2x+1+2), y_2 = 3x\\)

Explanation:

Identify the left and right sides of the equation

$$
LATEXBLOCK0
$$

Formulate the system of equations

$$
LATEXBLOCK1
$$

Match with the given options

$$ y_1 = \log(2x + 1), \quad y_2 = 3x - 2 $$

Answer:

• (A) \(y_1 = 3x, y_2 = 2x\)
• (B) \(y_1 = \log(2x + 1), y_2 = 3x - 2\) (Correct answer)
• (C) \(y_1 = \log 2x + 1, y_2 = 3x - 2\)
• (D) \(y_1 = \log(2x + 1 + 2), y_2 = 3x\)