What are the solutions of the following system? StartLayout Enlarged left-brace 1st row 10 x squared minus y = 48 2nd row 2 y = 16 x squared + 48 EndLayout

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)

(6, 312) and (-6, 312)