Different methods of solving systems
Answers are for parents and teachers.
1
Solve the system x + y + xy = 20, x + y − xy = −4.
(2, 6), (6, 2)
2
Solve the system x² + y² = 25, xy = 12.
(3, 4), (4, 3), (−3, −4), (−4, −3)
3
Solve the system x − y² = 2, xy² = 24.
(6, 2), (6, −2)
4
Solve the system x²y = 9, xy² = 3.
(3, 1)
5
Prove x² + y² = s² − 2p using (x + y)².
s² = (x + y)² = x² + 2xy + y² = x² + y² + 2p, so x² + y² = s² − 2p.