# Question #4112a

Oct 7, 2016

No solution

#### Explanation:

$\left\{\begin{matrix}2 x - 3 y = 6 \\ 6 x = 9 y + 9\end{matrix}\right.$

Dividing the second equation by $3$, we get

$\frac{6 x}{3} = \frac{9 y}{3} + \frac{9}{3}$

$\implies 2 x = 3 y + 3$

Substituting our new value for $2 x$ into the first equation, we get

$\left(3 y + 3\right) - 3 y = 6$

$\implies 3 = 6$

As this is a contradiction, no $\left(x , y\right)$ pair satisfies both given equations. The system has no solution.