Respuesta :
Answer:
[tex]x=3[/tex] & [tex]y=5[/tex]
Using the method of finding solution of linear equation in two variables and concept of exponent we found the solution.
Step-by-step explanation:
from the Question,
Given:-
[tex]b^{x}b^{y}= b^{8}[/tex]
[tex]b^{4x}b^{-2y} = b^{2}[/tex]
Using law of exponents we get,
[tex]x^{m} x^{n} = x^{m+n}[/tex] & [tex]x^{m} = x^{n}[/tex] ⇒ [tex]m = n[/tex]
Now, from the data given in the question,
⇒ [tex]b^{(x+y)} = b^{8}[/tex]
⇒ [tex](x+y) = 8[/tex] ..............(i)
⇒ [tex]b^{4x-2y} = b^{2}[/tex]
⇒ [tex]4x-2y = 2[/tex] ..............(ii)
Solving equation (i) & (ii) we get,
[tex]4\times(x+y) = 4\times8[/tex]
[tex](4x+4y) = 32[/tex] ...............(iii)
Subtracting equation (ii) from (iii) we get,
[tex]y=5[/tex]
Putting the value of in equation (i)
[tex]x=3.[/tex]
Using the method of finding solution of linear equation in two variables and concept of exponent we found the solution.
The values of x and y from the given expressions are; x = 3 and y = 5
We are given;
b^(x) × b^(y) = b^(8) - - - (eq 1)
b^(4x) × b^(-2y) = b^(2) - - - (eq 2)
- Now according to laws of exponents, we know that;
If a² × a³ = a^(y)
Then it means that;
2 + 3 = y
- Thus, from eq 1, we have;
x + y = 8 - - - (eq 3)
- From eq 2, we have;
4x - 2y = 2 - - - (eq 4)
From eq 3; x = 8 - y
Thus;
4(8 - y) - 2y = 2
32 - 4y - 2y = 2
30 = 6y
y = 30/6
y = 5
Thus;
x = 8 - 5
x = 3
Read more about simultaneous equations at;https://brainly.com/question/16863577
