Determine if the point (3, 8) is a solution to the simultaneous inequalities y > x + 5 and y ≤6x -3. Select the response that gives the correct answer as well as the correct reasoning.
• No, it is in the solution set for y < 6x - 3, but on the line for y > x + 5.
• Yes, because both of these inequalities include points on the line as a solution.
• Yes, it is within the solution set for both inequalities.
• No, it is not in the solution set for either inequality.
To determine if the point (3, 8) is a solution to the simultaneous inequalities y > x + 5 and y ≤6x -3, we need to substitute the x and y values of the point into both inequalities.
For the first inequality y > x + 5:
8 > 3 + 5
8 > 8
This is not true, so the point (3, 8) is not in the solution set for y > x + 5.
For the second inequality y ≤ 6x - 3:
8 ≤ 6(3) - 3
8 ≤ 18 - 3
8 ≤ 15
This is true, so the point (3, 8) is in the solution set for y ≤ 6x - 3.
Therefore, the correct answer is:
No, it is in the solution set for y ≤ 6x - 3, but on the line for y > x + 5.