Answer:To show that the two pairs of lines are parallel, we need to show that they have the same slope.
The first pair of lines is represented by:
x^2 - 4xy - 5y^2 = 0
This can be factored as:
(x - 5y)(x + y) = 0
Which gives us two lines:
x - 5y = 0 --> y = (1/5)x
x + y = 0 --> y = -x
The slopes of these lines are 1/5 and -1, respectively.
The second pair of lines is represented by:
x^2 - 4xy - 5y^2 - 2x - 2y = 0
This can be rearranged as:
x^2 - 4xy - 5y^2 = 2x + 2y
Subtracting 2x + 2y from both sides gives us:
x^2 - 4xy - 5y^2 - 2x - 2y = 0
Factoring the left-hand side gives us:
(x - 5y)(x + y) = 2(x + y)
Which gives us two lines:
x - 5y = 0 --> y = (1/5)x
x + y = 2 --> y = -x + 2
The slopes of these lines are also 1/5 and -1, respectively.
Since the slopes of the lines in both pairs are the same, the pairs of lines are parallel.
Step-by-step explanation: