Answer
$(3, -1/2)$
$(-3, -1/2)$
Work Step by Step
Given the system of equations:
1. $2x^2 - 8y^3 = 19$
2. $4x^2 + 16y^3 = 34$
It asks to find all solutions.
Double equation one, add the result to equation 2
$4x^2 - 16y^3 = 38$
+ ($4x^2 + 16y^3 = 34$)
$8x^2 = 72$
$x^2 = 9$
$x = 3, -3$
Substitute the values into the equation
$4(3)^2 + 16y^3 = 34$
$36 + 16y^3 = 34$
$y^3 = -1/8$
$y = -1/2$
$4(-3)^2 += 16y^3 = 34$
$36 + 16y^3 = 34$
$y^3 = -1/8$
$y = -1/2$
All solutions:
$(3, -1/2)$
$(-3, -1/2)$
