Question

The system of equations 3x + 9y^3= -21, 13y^3+4x=-1 has exactly one solution.

Answer 1

Answer:

$\huge\boxed{(-88,3)}$

Step-by-step explanation:

$\sf 3x + 9y^3 = -21$  -------------------------- (1)

$\sf 13y^3+4x= -1$  -------------------------- (2)

Multiply Eq. (1) by 13 and (2) by 9

Equation (1):

$\sf 13(3x+9y^3) = -21 * 13$

$\sf 39x + 117y^3=-273$ --------------------(3)

Equation (2):

$\sf 9(13y^3+4x) = -1* 9$

$\sf 117y^3 + 36x = -9$ ------------------------(4)

Subtract Eq. (2) from (1)

$\sf 39x+117y^3-117y^3 -36x=-273+9$  

39x - 36x = -264

3x = -264

Dividing both sides by 3

x = -88

$\rule[225]{225}{2}$

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

$\rule[225]{225}{2}$

Ordered Pair = (x,y) = (-88,3)

$\rule[225]{225}{2}$

Hope this helped!

~AnonymousHelper1807