Solve: 8x . 4y = 128 , 92 x - y = 1

The correct answer is: Value of x & y for the given equations are 1 & 2, respectively

Step-by-step solution:-
8_x . 4y = 128 …........................................ (Equation i)
9^2x-y = 1
∴ 9^2x-y = 90 …........................................... (b⁰ = 1)
∴ 2x - y = 0 …............................................ (Exponents of the same base of an equation are equal)
∴ 2x = y ............................................... (Equation ii)
Substituting Equation ii in Equation i, we get-
8^x . 4^y = 128
∴ 8^x . 4^2x = 128
∴ (2³)x × (22)2x = 128
∴ 2³x × 2^4x = 128 .............................. [(bⁿ)m = b^nm]
∴ 2^3x+4x = 128 .............................. (aⁿ × a^m = a^n+m)
∴ 2⁷x = 27
∴ 7x = 7 .................................. (Exponents of the same base in an equation are equal)
∴ x = 1 ................................... (Dividing both the sides by 7) ............................................ (Equation iii)
Substituting Equation iii in ii, we get-
2x = y
∴ 2 (1) = y
∴ 2 = y
i.e. y = 2
Final Answer:-
∴ Value of x & y for the given equations are 1 & 2, respectively.