Question

Can someone please help solve these simultaneous equations?
a.) 2^x+y=8
3^2x-y=27
b.) 3^y+x=9^y+x
2^x-y=8^x-3
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Answer 1

Answer:

a) x = 2, y = 1

b) x = 9, y = -9

Step-by-step explanation:

a)     $2^{x+y} = 8$

   ⇒ $2^{x+y} = 2^{3}$

   ⇒ $x+y = 3$

and

      $3^{2x-y} = 27$

  ⇒ $3^{2x-y} = 3^{3$

  ⇒ $2x-y = 3$

By solving the above two equations, we get;

x = 2 and y = 1

b)     $3^{y+x} = 9^{y+x}$

   ⇒ $3^{y+x} = 3^{2y+2x}$

   ⇒ $x=-y$

and

       $2^{x-y} = 8^{x-3}$

   ⇒ $2^{x-y} = 2^{3x-9}$

   ⇒ $2x + y=9$

By solving the above two equations, we get;

x = 9 and y = -9