What are the solutions of the following system?

The correct answer is: (6, 312), (-6, 312)

Step-by-step explanation:

This is a system of two square equations with two unknowns x and y

We will solve this system in the next way:

2 y = 16 x² + 48  

First we will divide this equation with number 2, the both sides and get:

y = 8 x² + 24  =>  8 x² - y = - 24

10 x² - y = 48  and   8 x² - y = - 24

Now we will subtract the second equation from the first and get, the both sides:

10 x² - 8 x² - y - (-y) = 48 - ( - 24)  => 2 x² = 72  => x² = 72/2 = 36

x = √36  =>  x₁ = 6  and  x₂ = - 6

now we will replace  this solutions in this equation  8 x² - y = - 24 and get:

8 · 6² - y = - 24  => 8 · 36 - y = - 24 =>  288 - y = - 24 => y₁ = 288 + 24 = 312

8 · (-6)² - y = - 24  => 8 · 36 - y = - 24 =>  288 - y = - 24 => y₂ = 288 + 24 = 312

We have that y₁ = y₂ = 312

We have two pairs of solutions:

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

God with you!!!

answer is : muchas/tipicas

have a nice day!

~recklesschicken