Answer:
To solve the equation x^2 - y^2 - 3x - 3y = 0, we can try to factor it:
x^2 - y^2 - 3x - 3y = 0
We can see that this is a difference of squares (x^2 - y^2), which can be factored as (x + y)(x - y). So, we have:
(x + y)(x - y) - 3(x + y) = 0
Now, we can factor out the common factor of (x + y):
(x + y)[(x - y) - 3] = 0
Now, we have two factors to consider:
1. (x + y) = 0
2. (x - y) - 3 = 0
Let's solve each equation separately:
1. (x + y) = 0
x + y = 0
x = -y
2. (x - y) - 3 = 0
x - y = 3
x = 3 + y
So, we have two possible solutions for x:
a) x = -y
c) x = 3 + y
Therefore, the correct options are:
a) x = -y
c) x = 3 + y
Explanation: