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The boundary for the first inequality: y> x+3 is the line y=x+3 and will be excluded (dashed) from the highlighted area because of the absence of equality sign.
The boundary for the second inequality: y <= 3x-3 is the line y=3x-3, and will show in solid because of the presence of the equal sign.
Please see the image attached showing your original graph with the first inequality in blue, the second in red. Note the y intercepts highlighted by a dot, and also verify the slopes: 1 and 3, respectively.
The solution to the system if inequalities is the area with both shadings overlapping.
Let me know if you have questions.
