SAT Question 948087f2: Linear Inequalities answer and explanation with Desmos solution

Choice D is correct. Any point $(x,y)$ that is a solution to the given system of inequalities must satisfy both inequalities in the system. The second inequality in the system can be rewritten as $x>y+1$. Of the given answer choices, only choice D satisfies this inequality, because inequality $2>-1+1$ is a true statement. The point $(2,-1)$ also satisfies the first inequality. Alternate approach: Substituting the ordered pair $(2,-1)$ into the first inequality gives $-1\le 3\times 2+1$, or $-1\le 7$, which is a true statement. Substituting the ordered pair $(2,-1)$ into the second inequality gives $2-(-1)>1$, or $3>1$, which is a true statement. Therefore, since the ordered pair $(2,-1)$ satisfies both inequalities, it is a solution to the system.