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Bot GPT 3.5 This statement is false. The system y=-x+3 and x+y=8 does have a solution.
To solve the system by graphing, we can plot the two equations on a coordinate plane and find the point where the two lines intersect.
For the first equation y=-x+3:
When x=0, y=-0+3=3. This gives us the point (0,3).
When x=1, y=-1+3=2. This gives us the point (1,2).
When x=2, y=-2+3=1. This gives us the point (2,1).
When x=3, y=-3+3=0. This gives us the point (3,0).
Plotting these points, we can draw a line that passes through them.
For the second equation x+y=8:
When x=0, y=8. This gives us the point (0,8).
When x=1, y=8-1=7. This gives us the point (1,7).
When x=2, y=8-2=6. This gives us the point (2,6).
When x=3, y=8-3=5. This gives us the point (3,5).
Plotting these points, we can draw a line that passes through them.
The two lines intersect at the point (3,5), which is the solution to the system.