2, 3): YES
(3, 4): YES
(0, 4): NO (for strict inequality, YES for non-strict inequality)
(10, 0): NO
(-2, 6): YES
(1, 3): YES
The inequality in the image is y > -x + 4. We can solve for y to get an idea of what the solution set looks like.
Adding x to both sides, we get:
y + x > 4
Then, subtracting 4 from both sides, we get:
y + x - 4 > 0
This can be rewritten as:
y > -x + 4
This is the same inequality as the one in the image, so we know that the solution set is all the points above the line y = -x + 4.
Now let's look at the points in the image:
(2, 3): This point is above the line, so yes, it is included in the solution set.
(3, 4): This point is also above the line, so yes, it is included in the solution set.
(0, 4): This point is on the line, so it is technically not part of the solution set for the strict inequality y > -x + 4. However, it would be included in the solution set for the non-strict inequality y ≥ -x + 4.
(10, 0): This point is below the line, so no, it is not included in the solution set.
(-2, 6): This point is above the line, so yes, it is included in the solution set.
(1, 3): This point is above the line, so yes, it is included in the solution set.
Therefore, the answers are:
(2, 3): YES
(3, 4): YES
(0, 4): NO (for strict inequality, YES for non-strict inequality)
(10, 0): NO
(-2, 6): YES
(1, 3): YES