[tex]x-\ amount\ of\ 2-bedroom\\
y-\ amount\ of \ 3-bedroom\\\\
x+y=6\ \ -->x=6-y\\
4600=x*700+y*900\\\\
4600=700(6-y)+900y\\\\
4600=4200-700y+900y\\\\
4600-4200=200y\\\\
400=200y\ |:200\\\\y=2\\x=6-y=6-2=4\\\\ Two\ 2-bedroom\ apartaments\ and\ four\ 3-bedroom\ apartaments\\were\ vacant,[/tex]