Consider the point $P=(1,2)$ in $R^2$ and the vector $v=($:$-4,-2$:$).$

$($a$)($ : 'Write an equation for the line that passes through $P$ and is parallel to $v.$

$($b$)$ Write an equation for the line that passes through $P$ and is orthogonal to $v.$

$($ Solve the system of equations

$-2x+y+3z=-7$

$3x+2y-z=0$

$x+4y+2z=-9$