Question

Solve the equation x^2 - y^2 - 3x - 3y. a) x = y b) x = -y c) x = 3 + 3y d) x = -3 + 3y

Answer 1

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: