Answer:
[tex]\huge\boxed{(-88,3)}[/tex]
Step-by-step explanation:
[tex]\sf 3x + 9y^3 = -21[/tex] -------------------------- (1)
[tex]\sf 13y^3+4x= -1[/tex] -------------------------- (2)
Multiply Eq. (1) by 13 and (2) by 9
Equation (1):
[tex]\sf 13(3x+9y^3) = -21 * 13[/tex]
[tex]\sf 39x + 117y^3=-273[/tex] --------------------(3)
Equation (2):
[tex]\sf 9(13y^3+4x) = -1* 9[/tex]
[tex]\sf 117y^3 + 36x = -9[/tex] ------------------------(4)
Subtract Eq. (2) from (1)
[tex]\sf 39x+117y^3-117y^3 -36x=-273+9[/tex]
39x - 36x = -264
3x = -264
Dividing both sides by 3
x = -88
[tex]\rule[225]{225}{2}[/tex]
Put x = -88 in Eq. (1)
3(-88)+9y³ = -21
-264 + 9y³ = -21
9y³ = -21 + 264
9y³ = 243
Dividing both sides by 9
y³ = 27
Taking cube root on both sides
y = 3
[tex]\rule[225]{225}{2}[/tex]
Ordered Pair = (x,y) = (-88,3)
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
