SATMathematics Practice Test 1

To determine which quadrant does not contain any solutions to the system of inequalities, graph the inequalities.
Graph the inequality $\mathit{y}\ge 2\mathit{x}+1$ by drawing a line through the y-intercept $\left(0,1\right)$ and the point $\left(1,3\right)$, and graph the inequality $\mathit{y}>12\mathit{x}-1$ by drawing a dashed line through the y-intercept $\left(0,-1\right)$ and the point $\left(2,0\right)$, as shown in the figure below.
The solution to the system of inequalities is the intersection of the shaded regions above the graphs of both lines. It can be seen that the solutions only include points in quadrants I, II, and III and do not include any points in quadrant IV.
Choices A and B are incorrect because quadrants II and III contain solutions to the system of inequalities, as shown in the figure above. Choice D is incorrect because there are no solutions in quadrant IV.