Answer:
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Given is the system of equations.
Solve it by substitution, x = y + 5:
- 8x² + 5y² = 40
- 8(y + 5)² + 5y² = 40
- 8(y² + 10y + 25) + 5y² = 40
- 8y² + 80y + 200 + 5y² = 40
- 13y² + 80y - 160 = 0
Find the discriminant of the quadratic equation, if it is positive there are two real solutions, if zero then one solution, if negative then no solution.
- D = 80² - 4*13*(-160)
- D = 14720
Since D > 0 there are two real solutions (intersections).