SAT Question 570b5a5d: Systems of Linear Equations answer and explanation with Desmos solution

Choice D is correct. Multiplying the second equation in the given system by $2$ yields $\frac{10}{2}x+12y=46$. Adding this equation to the first equation in the system yields $\left(\frac{7}{2}x+6y\right)+\left(\frac{10}{2}x+12y\right)=25+46$, which is equivalent to $\left(\frac{7}{2}x+\frac{10}{2}x\right)+\left(6y+12y\right)=25+46$, or $\frac{17}{2}x+18y=71$. Therefore, the value of $\frac{17}{2}x+18y$ is $71$.