Question

How to find X and Y for - x + 1 /2 + y - 1 /2 = 8 x - 1/3 + y + 1/2 =9 ​

Answer 1

Step-by-step explanation:

$- x + \frac{1}{2} + y - \frac{1}{2} = 8 x - \frac{1}{3} + y + \frac{1}{2} =9 \\ \\ can \: be \: written \: as \\ \\ - x + \frac{1}{2} + y - \frac{1}{2} = 9 \\ and \\ 8 x - \frac{1}{3} + y + \frac{1}{2} =9$

$- x + \frac{1}{2} + y - \frac{1}{2} = 9 \\ - x + y = 9 \: \: \: \: \: ...(1)$

$8 x - \frac{1}{3} + y + \frac{1}{2} =9 \\ 8x - y - ( \frac{1}{3} - \frac{1}{2}) = 9 \\ 8x - y - ( \frac{2 - 3}{6}) = 9 \\ 8x - y + \frac{1}{6} = 9 \\8x - y = 9 - \frac{1}{6} \\ 8x - y = \frac{53}{6} \: \: \: \: \: \: \: \: ...(2)$

Solving (1) and (2)

$- x + y = 9 \\ 8x - y = \frac{53}{6} \\ - - - - - - - \\ 7x = 9 + \frac{53}{6} \\ 7x = \frac{107}{6} \\ x = \frac{107}{42}$

Hence,

$- \frac{107}{42} + y = 9 \\ y = 9 + \frac{107}{42} \\ y = \frac{378 + 107}{42} = \frac{485}{42}$