SAT Mathematics Practice Test 3

The inequalities $\mathit{y}\le -15\mathit{x}+3000$ and$\mathit{y}\le 5\mathit{x}$ can  be graphed in the xy-plane.
They are represented by the half-planes below and include the boundary lines $\mathit{y}=-15\mathit{x}+3000$ and $\mathit{y}=5\mathit{x}$,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: $5\mathit{x}=-15\mathit{x}+3000$, which has solution $\mathit{x}=150$.
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 $5\left(150\right)=-15\left(150\right)+3000=750$.
This is the maximum possible value of b for a point $\left(\mathit{a},\mathit{b}\right)$ that is in the solution set of the system of inequalities.