Xavier Aptitude Test 2019 Paper

$3\mathit{x}+4\mathit{y}=2\mathit{a}$...(i)
and $7\mathit{x}+2\mathit{y}=2018$ ...(ii)
Point of intersection = P
From (i) and (ii),
$-4\mathit{x}+2\mathit{y}=2\mathit{a}-2018$
$\Rightarrow \mathit{y}-2\mathit{x}=\mathit{a}-1009$ ...(iii)
Now $3\mathit{x}+4\mathit{y}=2018$ ... (iv)
Point of intersection = Q
and $5\mathit{x}+3\mathit{y}=1$ ... (v)
From (iv) and (v),
$\mathit{x}=-550,\mathit{y}=917$
$\Rightarrow \mathit{Q}=\left(-550,917\right)$
Slope of line joining P (x, y) and Q (-550, 917)
$\frac{\mathit{y}-917}{\mathit{x}+550}=2$
$\Rightarrow \mathit{y}-917=2\mathit{x}+1100$
$\Rightarrow \mathit{y}-2\mathit{x}=2017$ ...(vi)
From (iii) and (vi),
$\mathit{a}-1009=2017$ $\Rightarrow \mathit{a}=3026$