Question

6 x minus 5 y equals to 8 and minus 12 x + 2 y equals to zero solve by substitution method​

Answer 1

Answer:

$x = \frac{2}{9} \ and \ y = \frac{-4}{3}$

Step-by-step explanation:

It is given that

$6x - 5y = 8.......(1)\\12x \ + 2y = 0....(2)\\In \ (1)\\6x - 5y = 8\\6x = 8 + 5y\\\\x = \frac{8 \ + \ 5y}{6}\\putting \ above \ value \ in \ (2)\\12x \ + \ 2y = 0\\12(\frac{8 \ + \ 5y}{6}) \ + \ 2y = 0\\\\2(\frac{8 \ + \ 5y}{1}) \ + \ 2y = 0\\\\2(8 \ + \ 5y) + 2y = 0\\16 + 10y + 2y = 0\\16 + 12y = 0\\12y = -16\\y = \frac{-16}{12} = \frac{-4}{3}\\Now \ using \ (1)\\x = \frac{8 \ + \ 5y}{6} = \frac{8 \ + \ 5(\frac{-4}{3}\\)}{6} = \frac{8 \ + \ (\frac{-20}{3}\\)}{6}$

$\frac{\frac{24 - 20}{3}}{6} = \frac{\frac{4}{3}}{6} = \frac{4}{18} \\\\= \frac{2}{9}$

Therefore,

$x = \frac{2}{9} \ and \ y = \frac{-4}{3}$