Answer:
Required ordered pair is (0,0) for system of equation
Step-by-step explanation:
The given system of equation is
A). [tex]9^{12x} = 9^{3y}[/tex]
B). [tex]y^{4} - 9y^{2} x^{2} =16y[/tex]
On simplifying the equation A
[tex]9^{12x} = 9^{3y}[/tex]
Take log on both side,
(12x) (log9) = (3y) (log9)
4x=y
To find the solution of the system of the equation :
Replacing value of y=4x in equation B,
[tex]y^{4} - 9y^{2} x^{2} =16y[/tex]
[tex](4x)^{4} - 9(4x)^{2} x^{2} =16(4x)[/tex]
[tex]256x^{4} - 144x^{2} x^{2} =64x[/tex]
[tex]256x^{4} - 144x^{4}=64x[/tex]
[tex]112x^{4}=64x[/tex]
We get,
x=0 and x=0.829
Since, 0.829 is not integer number
Only solution of equations is x=0
For the value of y
Replace value x in y=4x=0
Thus, Required ordered pair is (0,0)
