Answer
$(1,2)$
Work Step by Step
Please see the screenshot of the tables for the two equations.
Green line: $x+3y=7$
Purple line: $2x-3y=-4$
If we replace $x$ and $y$ with $1$ and $2$, respectively, for the green line, we have
$x+3y=7$
$1+3*2=7$
$1+6=7$ (true)
Purple line:
$2x-3y=-4$
$2*1-3*2=-4$
$2-6=-4$ (true)
Purple line:
$2x-3y=-4$
$2x-3y+3y+4=-4+3y+4$
$2x+4=3y$
$(2x+4)/3=3y/3$
$2/3*x+4/3=y$ ($m=2/3$, y-intercept is 4/3)
Green line:
$x+3y=7$
$3y=7-x$
$3y/3=(7-x)/3$
$y=7/3-1/3*x$
$y=-1/3*x+7/3$ ($m=-1/3$, y-intercept is 7/3)