Answer
$\{(2,4)\}$.
Work Step by Step
First equation $x+y=6$.
Plug $y=0$ into the equation.
$\Rightarrow x+0=6$
$\Rightarrow x=6$
$x−$ intercept $A=(6,0)$.
Plug $x=0$ into the equation.
$\Rightarrow 0+y=6$
$\Rightarrow y=6$
$y−$ intercept $B=(0,6)$.
Now the second equation $4x-y=4$.
Plug $y=0$ into the equation.
$\Rightarrow 4x-0=4$
$\Rightarrow 4x=4$
$\Rightarrow x=1$
$x−$ intercept $C=(1,0)$.
Plug $x=0$ into the equation.
$\Rightarrow 4(0)-y=4$
$\Rightarrow -y=4$
$\Rightarrow y=-4$
$y−$ intercept $D=(0,-4)$.
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 $E=\{(2,4)\}$.
