SAT Mathematics Practice Test 3

The inequalities $y \leq -15x+3000$ and$y \leq 5x$ can  be graphed in the xy-plane. They are represented by the half-planes below and include the boundary lines $y = -15x+3000$ and $y = 5x$,respectively. The solution set of the system of inequalities will be the intersection of these half-planes, including the boundary lines, and the solution (a, b) with the greatest possible value of b will be the point of intersection of the boundary lines. The intersection of boundary lines of these inequalities can be found by setting them equal to each other: $5x = -15x+3000$, which has solution $x = 150$. Thus, the x-coordinate of the point of intersection is 150. Therefore, the y-coordinate of the point of intersection of the boundary lines is $5(150) = -15(150) + 3000 = 750$. This is the maximum possible value of b for a point $(a, b)$ that is in the solution set of the system of inequalities.