Solve-simultaneously-x-y-5-i-5-x-y-15-ii-

Question Number 18388 by tawa tawa last updated on 19/Jul/17

Solve simultaneously .

x + y = 5 \dots \dots . (i)

5^{x} + y = 15 \dots \dots (ii)

Answered by mrW1 last updated on 19/Jul/17

5^{x} - x = 10

5^{x} = x + 10

5^{x + 10} = (x + 10) 5^{10}

e^{(x + 10) \ln 5} = (x + 10) 5^{10}

- (x + 10) \ln {5 e}^{- (x + 10) \ln 5} = - 5^{- 10} \ln 5

- (x + 10) \ln 5 = W (- 5^{- 10} \ln 5)

\Rightarrow x = - \frac{W (- 5^{- 10} \ln 5)}{\ln 5} - 10 \approx - 10

\Rightarrow y = \frac{W (- 5^{- 10} \ln 5)}{\ln 5} + 15 \approx 15

Commented by tawa tawa last updated on 19/Jul/17

God bless you sir .