Verified answer

[tex]\displaystyle \left \{ {{5y-4x=-7} \atop {5y+x=2}} \right.\\ \\\left \{ {{-4x+5y=-7} \atop {x+5y=2}} \right.\\ \\(-4x+5y)-(x+5y)=-7-2\\-5x=-9\\\\x=\frac{9}{5}\\ \\-4(\frac{9}{5})+5y=-7\\ \\y=\frac{1}{25}\\ \\(x,y)=(\frac{9}{5},\frac{1}{25})[/tex]