SAT Question 30b1e186: Linear Inequalities answer and explanation with Desmos solution

Choice D is correct. It’s given that the solution set consists of points in the xy-plane where $5x-7y>35$, which can also be written as $5x+(-7y)>35$. If $(x,y)$ is a point in the region where $x<0$ and $y>0$, then $x$ is a negative number and $y$ is a positive number. If $x$ is a negative number, then the value of $5x$ is a negative number. If $y$ is a positive number, then the value of $-7y$ is a negative number. It follows that the expression $5x+(-7y)$ is the sum of two negative numbers and is therefore negative. If the value of $5x+(-7y)$ is negative, then the value of $5x+(-7y)$ cannot be greater than $35$. Thus, the region where $x<0$ and $y>0$ does not contain any points that are part of the solution set to $5x-7y>35$.