Answer:
The error is in the student's work when converting the standard form equation, 2x+2y=12 into a slope-intercept equation. The equation y=x+6 should have a negative slope. This is because in the first step for converting the standard form equation to slope intercept form, 2x was subtracted from both sides. This would make the equation in the 2nd step 2y=-2x+12. When 2 was divided from both sides, the equation should have become y=-x+6. The solution for the system of equations is the point (4,2), meaning there is one solution. The line y=x-2 would be plotted the same. The line y=-x+6 would have the same y-intercept, but a negative slope of 1, so instead of the line going up by 1 and to the right by 1, it would go down by 1 and to the right by 1 and intersect y=x-2 at (4,2).