Answer:
The solutions of the system ⇒ (-6 , 312) and (6 , 312)
Step-by-step explanation:
Given:
10x² - y = 48 ⇒(1)
2y = 16x² + 48 ⇒(2)
From eq.(1) ⇒ y = 10x² - 48 ⇒(3)
By substitution with y from eq.(3) at eq.(2)
∴ 2(10x² - 48) = 16x² + 48
Solve for x
∴ 20x² - 96 = 16x² + 48
∴ 20x² - 16x² = 48 + 96
∴ 4x² = 144
∴ x² = 144/4 = 36
∴ x = ±√36 = ±6
By substitution with x at eq.(3)
when x = 6 ⇒ y = 10x² - 48 = 10 * 6² - 48 = 10 * 36 - 48 = 312
when x = -6 ⇒ y = 10x² - 48 = 10 * (-6)² - 48 = 10 * 36 - 48 = 312
So, there are two solutions of the system which are (-6,312) and (6,312)
