Answer
$(1,2)$.
Work Step by Step
First equation $2x+y=4$.
Plug $y=0$ into the equation.
$2x+0=4$
$2x=4$
$x=2$
$x-$ intercept $A=(2,0)$.
Plug $x=0$ into the equation.
$2(0)+y=4$
$0+y=4$
$y=4$
$y-$ intercept $B=(0,4)$.
Now for the second equation $4x+3y=10$.
Plug $y=0$ into the equation.
$4x+3(0)=10$
$4x+0=10$
$4x=10$
$x=\frac{10}{4}$
$x=\frac{5}{2}$
$x-$ intercept $C=(\frac{5}{2},0)$.
Plug $x=0$ into the equation.
$4(0)+3y=10$
$0+3y=10$
$3y=10$
$y=\frac{10}{3}$
$y-$ intercept $D=(0,\frac{10}{3})$.
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 $(1,2)$.
