Xr==xr*Yr/yr
Zr==(1-xr-yr)*Yr/yr
Xg==xg*Yg/yg
Zg==(1-xg-yg)*Yg/yg
Xb==xb*Yb/yb
Zb==(1-xb-yb)*Yb/yb

Xv==xb*Yb/yb+xg*Yg/yg+xr*Yr/yr
Yv==Yb+Yg+Yr
Zv==(1-xb-yb)*Yb/yb+(1-xg-yg)*Yg/yg+(1-xr-yr)*Yr/yr

FullSimplify[xv==(xb*Ybv/yb+xg*Ygv/yg+xr*Yrv/yr)/(xb*Ybv/yb+xg*Ygv/yg+xr*Yrv/yr+Ybv+Ygv+Yrv+(1-xb-yb)*Ybv/yb+(1-xg-yg)*Ygv/yg+(1-xr-yr)*Yrv/yr)]
FullSimplify[yv==(Ybv+Ygv+Yrv)/(xb*Ybv/yb+xg*Ygv/yg+xr*Yrv/yr+Ybv+Ygv+Yrv+(1-xb-yb)*Ybv/yb+(1-xg-yg)*Ygv/yg+(1-xr-yr)*Yrv/yr)]//Factor