SAT Question c5082ce3: Systems of Linear Equations answer and explanation with Desmos solution

Let $x$ represent the number of correct answers from the player and $y$ represent the number of incorrect answers from the player. Since the player answered $40$ questions in total, the equation $x+y=40$ represents this situation. Also, since the score is found by subtracting the number of incorrect answers from twice the number of correct answers and the player received a score of $50$, the equation $2x-y=50$ represents this situation. Adding the equations in the system of two equations together yields $(x+y)+(2x-y)=40+50$. This can be rewritten as $3x=90$. Finally, solving for $x$ by dividing both sides of the equation by $3$ yields $x=30$.