Answer
The student's error was not providing a wide enough graph to see the intersection point (-4,7)
Work Step by Step
Because the equations y=-x+3 and y=-2x-1 have different slopes, we know that they will eventually intersect at some point, but the student could not see this because the window chosen was not large enough.
One method for solving, is to set both equations equal to each other:
$-x+3 =-2x-1 \\ x+3=-1 \\ x=-4$
Plug the value of x back into the original equation of choosing to obtain the y-value:
$y= -(-4)+3\\
y=7$
Now that we have our x and y value, we can identify our point of intersection as (-4,7)
