Solve simultaneously..? x = 3^y and x = 1/2 (3 + 9y)

1 Answer
Jumbotron
Nov 23, 2017

This is the method I used in deducing the following simultaneously equation..

See steps below;

Explanation:

Solving simultaneously..

x = 3^y - - - - - - eqn1

x = 1/2(3 + 9y) - - - - - - eqn2

Look at the common value in both equations..

x is the common, hence we equate both together..

Having..

3^y = 1/2(3 + 9y)

3^y = (3 + 9y)/2

Cross multiplying..

3^y/1 = (3 + 9y)/2

2xx 3^y = 3 + 9y

6^y = 3 + 9y

Log both sides..

log6^y = log(3 + 9y)

Recall the law of logarithm -> log6^y = x, ylog6 = x

Therefore...

ylog6 = log(3 + 9y)

Divide both sides by log6

(ylog6)/(log6) = log(3 + 9y)/(log6)

(ycancel(log6))/cancel(log6) = log(3 + 9y)/(log6)

y = (log(3 + 9y))/log(6)

y = (cancel (log)(3 + 9y))/(cancel (log)(6))

y = (3 + 9y)/6

Cross multiplying..

y/1 = (3 + 9y)/6

6 xx y = 3 + 9y

6y = 3 + 9y

Collect like terms

6y - 9y = 3

-3y = 3

Divide both sides by -3

(-3y)/(-3) = 3/-3

(cancel(-3)y)/cancel(-3) = 3/-3

y = -3/3

y = - 1

Substitute the value of y into eqn1 to get x

x = 3^y - - - - - - eqn1

x = 3^-1

Recall in indices, x^-1 = 1/x

:. x = 1/3

Hence the values are rArr x = 1/3, y = -1

Hope this helps!

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