In a rectangular coordinate system, the line $3y = x$ intersects the line $2x + 5y = 11$ at point $A$. What is the sum of the coordinates of point $A$? Please do a full walkthrough.
+2666 We have the system:
\(2x + 5y = 11 \ \ \ \ \ \ \ (i)\)
\(3y = x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (ii)\)
Start by substituting \((ii)\) into \((i)\), which gives us \(2(3y) + 5y = 11\), meaning \(y = 1\)
Now, plug in \(y = 1\) into \((ii)\), to get \(3 \times 1 = x\), meaning \(x = 3\).
This means that the solution is \((3,1) \), meaning the sum is \(3 + 1 = \color{brown}\boxed{4}\)
