Simple systems with a second-degree equation
Answers are for parents and teachers.
1
Solve the system x + y = 8, xy = 15.
(3, 5), (5, 3)
2
Solve the system x − y = 4, x² + y² = 40.
(6, 2), (−2, −6)
3
Solve the system x² − y² = 24, x − y = 4.
(5, 1)
4
Find two numbers with sum 13 and product 36.
4 and 9
5
A rectangle has perimeter 18 m and area 20 m². Find its sides and explain the method.
x + y = 9, xy = 20, z² − 9z + 20 = 0: the sides are 4 m and 5 m.