Answer
Since the point $(-2, 3)$ is a solution of the three equations, all three equations intersect at this one point.
Work Step by Step
$x+y=1$
$x+y-x=1-x$
$y= -x+1$
$y=0$
$x+y=1$
$x+0=1$
$x=1$
This line has a slope of -1, an x-intercept of 1, and a y-intercept of 1.
$2x-y=-7$
$2x-y+y+7=-7+y+7$
$2x+7=y$
$y=0$
$2x-y=-7$
$2x-0=-7$
$2x=-7$
$2x/2= -7/2$
$x=-7/2$
This line has a slope of 2, an x-intercept of -7/2, and a y-intercept of 7.
$x+3y=7$
$x+3y-x=7-x$
$3y=-x+7$
$3y/3=(-x+7)/3$
$y= -1/3*x+7/3$
$y=0$
$x+3y=7$
$x+3*0=7$
$x+0=7$
$x=7$
This line has a slope of -1/3, an x-intercept of 7, and a y-intercept of 7/3.