The system of equations $4x + 6y = 5$ and $8x + 12y = 10$ has

Let the line $2x + 3y = 18$ intersect the $Y$-axis at $B$. Suppose $C(\neq B)$,with coordinates $(a, b)$,is a point on the line such that $PB = PC$,where $P = (10, 10)$. Then,$8a + 2b$ equals

$A$ straight line passing through $P(3, 1)$ meets the coordinate axes at $A$ and $B$. It is given that the distance of this straight line from the origin $O$ is maximum. The area of triangle $OAB$ is equal to

If the equation of the straight line passing through the point of intersection of $x+2y-19=0$ and $x-2y-3=0$ and which is at a perpendicular distance of $5$ units from the point $(-2,4)$ is $5x+by+c=0$,then a possible value of $5+b+c$ is

The area of the parallelogram formed by the lines $y = mx$,$y = mx + 1$,$y = nx$,and $y = nx + 1$ is equal to

$A$ straight line $x/a - y/b = 1$ passes through the point $(8, 6)$ and cuts a triangle of area $12 \text{ sq units}$ from the axes of coordinates. The equations of the straight lines are