Answer
$(2, 1)$
$(-2, 1)$
Work Step by Step
Given the system of equations:
1. $x^4 + y^3 = 17$
2. $3x^4 + 5y^3 = 53$
It asks to find all solutions.
Triple equation one, subtract the result from equation 2
$3x^4 + 5y^3 = 53$
- ($3x^4 + 3y^3 = 51$)
$2y^3 = 2$
$y^3 = 1$
$y = 1$
Substitute the values into the equation
$x^4 + 1^3 = 17$
$x^4= 16$
$x = -2, 2$
All solutions:
$(2, 1)$
$(-2, 1)$
