Answer
$(1,-5)$.
Work Step by Step
First equation $4x-y=9$.
Plug $y=0$ into the equation.
$4x-0=9$
$4x=9$
$x=\frac{9}{4}$
$x-$ intercept $A=(\frac{9}{4},0)$.
Plug $x=0$ into the equation.
$4(0)-y=9$
$0-y=9$
$y=-9$
$y-$ intercept $B=(0,-9)$.
Now for the second equation $x-3y=16$.
Plug $y=0$ into the equation.
$x-3(0)=16$
$x+0=16$
$x=16$
$x-$ intercept $C=(16,0)$.
Plug $x=0$ into the equation.
$0-3y=16$
$0-3y=16$
$-3y=16$
$y=-\frac{16}{3}$
$y-$ intercept $D=(0,-\frac{16}{3})$.
Draw two lines using intercept points.
Graph is shown below in the image.
The intersection point of both lines is the solution.
Here we have the intersection point at $(1,-5)$.