From the given equation
[tex]\begin{gathered} 2x+5y=3\ldots(1) \\ 3x-2y=14\ldots(2) \end{gathered}[/tex]Now,
from the equation (1)
[tex]\begin{gathered} 2x+5y=3 \\ 2x=3-5y \\ x=\frac{1}{2}(3-5y)\ldots(3) \end{gathered}[/tex]Then,
Put the value of x into the equation (2)
[tex]\begin{gathered} 3x-2y=14 \\ 3(\frac{3}{2}-\frac{5}{2}y)-2y=14 \\ \frac{9}{2}-\frac{15}{2}y-2y=14 \\ 9-15y-4y=28 \\ 9-19y=28 \\ -19y=28-9 \\ -19y=19 \\ y=-1 \end{gathered}[/tex]Then,
Put the value of y into the equation (3)
So,
[tex]\begin{gathered} x=\frac{1}{2}(3-5y) \\ x=\frac{1}{2}(3-5(-1)) \\ x=\frac{1}{2}(3+5) \\ x=\frac{8}{2} \\ x=4 \end{gathered}[/tex]Hence, the value of x is 4 and y is -1.