The pair of lines represented by the equation x^2 - 4xy + 3y^2 = 0 are:

The pair of lines represented by the equation x^2 - 4xy + 3y^2 = 0 are:

Step 1: Start with the given equation: x^2 - 4xy + 3y^2 = 0.
Step 2: This equation is a quadratic in terms of x and y, which can be factored to find the slopes of the lines.
Step 3: Rewrite the equation in the standard form: (x - ay)(x - by) = 0, where a and b are the slopes.
Step 4: To factor, we need to find two numbers that multiply to 3 (the coefficient of y^2) and add to -4 (the coefficient of xy).
Step 5: The numbers that work are -3 and -1, so we can factor the equation as (x - 3y)(x - y) = 0.
Step 6: From the factored form, we can see the slopes of the lines are 3 and 1 (from x = 3y and x = y).
Step 7: To check if the lines are perpendicular, calculate the product of the slopes: 3 * 1 = 3.
Step 8: Since the product of the slopes is not -1, the lines are not perpendicular.

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