A) Shading is below the line y=2x-7, and that line is dashed. Shading is above the line y=-x/2+3, and that line is solid. The solution area is where the shading overlaps.
B) No. It fails to satisfy the second inequality.
Part A. The boundary line of the first inequality has a slope of +2 and a y-intercept of -7. Since allowed y-values are less than those on this line, the line is dashed and the shading is below the line. The solution space is shown with blue shading in the attachment.
The boundary line of the second inequality has a slope of -1/2 and a y-intercept of +3. Allowed values of y are equal to or greater than those on this line, so the line is solid and shading is above the line. The solution space is shown with green shading in the attachment.
The solution space is where the shaded areas overlap, generally to the upper right of the graph.
Part B. The point (3, -7) is in the shaded area for the first inequality, but not for the second. It does not meet the requirement for y ≥ -1/2x +3. You can see this when you substitute the point values:
-7 ≥ -1/2(3) +3 ⇒ -7 ≥ 3/2 ⇒ FALSE
A. The first inequality has a dashed line with shading towards the bottom without the origin. The Second equation has a solid line with the shading towards the top without the origin.
B. Yes and No. The point is a solution to the second equation because it is in it's the shaded region. BUT it is not in the shaded region of both of them so it really isn't the solution to the system.
