X-y=4 xy=12

Solve the system: x − y = 4 xy = 12

From x − y = 4, x = y + 4. Substitute into xy = 12: (y + 4)y = 12 → y^2 + 4y − 12 = 0.

Factor: (y + 6)(y − 2) = 0 → y = 2 or y = −6.

Corresponding x:

• If y = 2, x = 6.
• If y = −6, x = −2.

Solutions: (x, y) = (6, 2) and (−2, −6).