\( (2,5) \) is solution of: \( 2 x+3 y=17 \) \( x+4 y=16 \)

To see why \( (2,5) \) is a solution, plug \( x = 2 \) and \( y = 5 \) into both equations. For the first equation: \( 2(2) + 3(5) = 4 + 15 = 19 \), which does not satisfy \( 17 \). However, substituting into the second equation gives \( 2 + 4(5) = 2 + 20 = 22 \), which also does not work. Looks like \( (2,5) \) is actually not a solution. In fact, you can use graphical methods to visualize these equations as lines on a coordinate plane. The point where the lines intersect is the solution to the system. Here, since you noted \( (2,5) \), it might be helpful to recalculate and see where those lines actually intersect!