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
​

Answer 1

a) x = 2, y = 1

b) x = 9, y = -9

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