Answer
$(0, 2/3)$
Please see the graph.
Work Step by Step
$y=1/2x+2/3$
$4x+6y=4$
Substitution
$4x+6y=4$
$4x+6(1/2*x+2/3)=4$
$4x+3x+4=4$
$7x+4=4$
$7x+4-4=4-4$
$7x=0$
$7x/7=0/7$
$x=0$
$y=1/2x+2/3$
$y=1/2*0+2/3$
$y=0+2/3$
$y=2/3$
Elimination
$y=1/2x+2/3$
$-6*y=-6*(1/2x+2/3)$
$-6y = -3x-4$
$-6y+3x+4=-3x-4+3x+4$
$-6y+3x+4 =0$
$4x+6y=4$
$4x+6y-4=4-4$
$4x+6y-4=0$
$4x+6y-4+(-6y+3x+4)=0+0$
$4x+6y-4-6y+3x+4=0$
$7x=0$
$7x/7=0/7$
$x=0$
$y=1/2x+2/3$
$y=1/2*0+2/3$
$y=0+2/3$
$y=2/3$