Solving two inequalities simultaneously

Q.

Maximize $Z=5x+3y$, subject to constraints $3x+5y\le 15,5x+2y\le 10,x\ge 0$ and $y\ge 0$.

Q. $y\le -15x+3000$
$y\le 5x$
In the xy plane, if a point with coordinates (a, b) lies in the solution set of the system of inequalities above, the maximum possible value of b is___

Q. If the system of inequalities $y\ge 2x+1$ and $y>\frac{1}{2}x-1$ is graphed in the xy-plane above, which quadrant contains no solutions to the system?

1. Quadrant II
2. Quadrant III
3. Quadrant IV
4. There are solutions in all four quadrants

Q. $y\le 3x+1$
$x-y>1$
Which of the following ordered pairs (x, y) satisfies the system of inequalities above?

1. (1, 5)
2. (2, -1)
3. (-2, -1)
4. (-1, 3)