Question

solve 2x-3y = 6, x+y=1​

Answer 1

We have ,

$\to$2x - 3y = 6 ----- (i)

$\to$x + y = 1 ----- (ii)

Multiply equation (i) by 1 and equation (ii) by 2 , we get

$\to$2x - 3y = 6 ----- (iii)

$\to$2x + 2y = 2 ----- (iv)

Substrate equation (iii) and (iv) , we get

$\to \bold{2x - 3y - (2x + 2y) = 6 - 2} \\ \\ \to</p><p> \bold{2x - 3y - 2x - 2y = 4}</p><p> \\ \\ \to \bold{- 5y = 4} \\ \\ \to \bold{y = - \frac{4}{5} }$

Put the value of $\bold{y = \bold{- \frac{4}{5} }}$ in equation (ii) , we get

$\to\bold{x + ( - \frac{ 4}{5} ) = 1} \\ \\ \to \bold{ x - \frac{4}{5} = 1} \\ \\ \to \bold{x = 1 + \frac{4}{5}} \\ \\ \to\bold{x = \frac{9}{5} }$

$\bold{Hence \: , }\: \fbox{ \bold{x = \frac{9}{5} } } \: \: \: \: \bold{ and} \: \: \: \: \fbox{ \bold{y = - \frac{4}{5} }}$