Question

solve for x and y ,32base x+51base y and 23base x +42 base y =710. ,number bases interms of simultaneous equation​

Answer 1

`x = -348.5, y = 350.5`

Explanation:

32base x means
`3x + 2`

Similarly, 32base x+51base y equals to
`3x + 2 + 5y + 1 = 3x + 5y + 3`

and 23base x +42 base y means
`2x + 3 + 4y + 2 = 2x + 4y + 5`

As per the given condition,
`3x + 5y + 3 = 2x + 4y + 5\\x + y = 2`

Putting,
`y = 2 - x` in
`2x + 4y + 5 = 710`, we get

`2x + 4y = 705\\2x + 4(2 - x) = 705\\8 - 2x = 705\\4 - x = 352.5\\x = -348.5`

`y = 2 - x = 2 - (-348.5) = 2 + 348.5 = 350.5`