Final answer:
Graphing the line 2x - 3y = 5 and determining the solution region shows that the point (1,5) does not satisfy the inequality 2x - 3y ≥ 5, as when substituted it gives an untrue statement.
Step-by-step explanation:
To demonstrate whether the point (1,5) satisfies the inequality 2x - 3y ≥ 5, we can start by graphing the boundary of the inequality, which is the line 2x - 3y = 5. Then, we need to determine which side of the line represents the solution to the inequality.
First, we graph the line by finding two points that satisfy the equation 2x - 3y = 5. If we let x = 0, then -3y = 5 and y = -5/3, which gives us the point (0, -5/3). If we let y = 0, then 2x = 5 and x = 5/2, giving us the point (5/2, 0). We can plot these points and draw the line through them.
Next, to determine which side of the line contains the solutions to the inequality, we can pick a test point (not on the line). A common choice is the origin (0,0), which when substituted into the inequality 2x - 3y ≥ 5 gives us 0 ≥ 5, which is not true. Therefore, the origin is not part of the solution set, and the side of the line opposite to where the origin lies is where the inequality holds true.
To check if the point (1,5) is in the solution set, we substitute it into the inequality: 2(1) - 3(5) ≥ 5, which simplifies to 2 - 15 ≥ 5, or -13 ≥ 5, which is not true. Thus, the point (1,5) does not satisfy the inequality, and the graphical representation shows it lies on the side of the line that does not represent the solution set.