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Maths-
General
Easy
Question
Solve: 8x.4y = 128 , 92x-y = 1
Hint:
In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent. an = a × a × ... × a n times.
The correct answer is: Value of x & y for the given equations are 1 & 2, respectively.
Step-by-step solution:- 8x . 4y = 128 …........................................ (Equation i) 92x-y = 1 ∴ 92x-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- 8x . 4y = 128 ∴ 8x . 42x = 128 ∴ (23)x × (22) 2x = 128 ∴ 23x × 24x = 128 .............................. [(bn)m = bnm] ∴ 23x+4x = 128 .............................. (an × am = an+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.