Simultaneous Equations With Indices

The simultaneous equations
Can most easily be solved by raising each equation to some power so that the powers of
( or
are equalised, then dividing the equations
Raise (1) to the power of 3 and (2) to the power of 2 giving
(3) divided by (4) gives
\[\frac{x^6y^9}{x^6y^4}=\frac{1125^3}{675^2} \rightarrow y^5=3125 \rightarrow y=\sqrt[5]{3125}=5\]

Then from (1)
\[x^25^3=1125 \rightarrow x^2=\frac{1125}{5^3}=9 \rightarrow x=\sqrt{9}=3\]

Only one square root is taken since
  does not fit equation (2)

Add comment

Security code