Verified answer

[tex]\displaystyle \left \{ {{\frac{x}{2}+\frac{y}{2}=2 } \atop {2x-3y=-5}} \right. \\\\-2(x+y)+(2x-3y)=-2*4-5\\-5y=-13\\\\y=\frac{13}{5}\\ \\x+\frac{13}{5}=4\\ \\x=\frac{7}{5}\\ \\(x,y)=(\frac{7}{5},\frac{13}{5})[/tex]