We have that
3x+5y=14
6x-4y=9
using a graph tool
see the attached figure
the exact solution is the point (2.41,1.36)
<span>1.(5/2, 4/3)-----> (2.5,1.33)--------> is the best approximation
2.(4/3, 5/2)------> (1.33,2.5)
3.(7/3, 7/2)------> (2.33,3.5)
</span>4.(-5/2,-7/5)----> (-2.5,-1.4)
the answer is
the estimate solution is the option
1.(5/2, 4/3)