Answer
$(x,y)=(3,\dfrac{1}{2})$; a unique solution
Work Step by Step
Since, we have two equations $5x-2y=14$ and $3x+4y=11$, we have
From the given two equations, we have $y=\dfrac{5x-14}{2}$
Plug the value of y in $3x+4y=11$, then$3x+4(\dfrac{5x-14}{2})=11$
or, $3x+10x=11+28$
or, $13x=39$
or, $x=3$
Now, $y=\dfrac{5x-14}{2}=\dfrac{5(3)-14}{2}=\dfrac{1}{2}$
Thus, $(x,y)=(3,\dfrac{1}{2})$; a unique solution