Final answer:
To solve the system of inequalities, y < 2x - 1 and y ≥ 10 - x, graph both inequalities and look for the overlapping region on the coordinate plane. Choose any point within this region to find a valid solution for the system.
Step-by-step explanation:
To solve the system of inequalities y < 2x - 1 and y ≥ 10 - x, we need to find a region on the coordinate plane where both conditions are satisfied. This involves a bit of graphing and identifying the intersection of the two areas defined by the inequalities. Let's start with the easier inequality, y ≥ 10 - x. This is a linear equation where the boundary line has a y-intercept at 10 and a slope of -1. All the points above and on this line satisfy the inequality. Secondly, for y < 2x - 1, the boundary line has a y-intercept at -1 and a slope of 2. The area below this line is the solution set for this inequality.
To find a solution that satisfies both inequalities, we can graph them on the same coordinate system and look for the overlapping region. Practically, this could involve shading the area above the first line and then shading below the second line to see where the shadings overlap. From this, we can pick any point in that overlapping region to be a solution to the system. For example, if we take x = 5, then from the first inequality y ≥ 5, and from the second one y < 9. Thus, any value for y such that 5 ≤ y < 9 is a solution to the system along with x = 5.