Find the magnitudes of the unknown forces if the sum of all forces is zero (figure)

Answer

`10/3; 25/3`

Explanation

Sum of all given forces =0
`:.xhat(i)-10hat(j)-15cos53^(@)+15sin53^(@)hat(j)`
`-ycos37^(@)hat(i)-ysin37^(@)hat(j)=0`
`xhat(i)-15xx3/5hat(i)-y*4/5hat(i)=0`..(i)
`-10hat(j)+15xx4/5hat(j)-y*3/5hat(j)=0`..(ii)
`x-4/5y-9=0` or `x-4/5y=9`
`-10+12-3/5y=0` or `3/5y=2` or `y=10/3`
and `x=9+4/5xx10/3=25/3`