Cookie policy · You can change your choice at any time on the page „Cookies“.

Accessibility

Text size
Read aloud

Your browser reads the text with the voice it has for this language.

Accessibility statement
Quiz

Year 3: Systems of quadratic equations in two unknowns

10 questions with solutions for year 3: a linear and a quadratic equation, homogeneous and symmetric systems – review problems.

Type the number or choose the right answer. When you finish, click Check answers and see the solutions.

1. Solve the system: 2x − 1 = y, 3x² = 4 − y²

2. Solve the system: y = 3x, x² + y² = 90

3. How many real solutions has the system x² + y² = 10, x² − 3xy + 2y² = 0?

4. Solve the system: x² + y² = 5, xy = −2

5. Solve the system: x² + y² = 26, xy = 5

6. Solve the system: x² + y² − 10 = 0, x + xy + y − 7 = 0

7. How many real solutions has the system x² + y² + x + y = 8, x² + y² + xy = 7?

8. x² + y² = 14, x² − y² = 10. What is x²?

9. 2x² + 3y² = 12, 5x² − 2y² = 11. What is y²?

10. Solve the system: 3x² − 4xy + y² = 0, x² + y² = 2