Let T, O and R represent the numbers of each flower (tulips, orchids, roses). T+O+R=300.
1.35T+4.75O+2.60R=766.60. R=14+O, O=R-14.
We can rewrite the equations by substituting for O:
T+2R-14=300; T+2R=314; T=314-2R.
Now substitute for T and O:
1.35(314-2R)+4.75(R-14)+2.60R=766.60.
423.90-2.70R+4.75R-66.50+2.60R=766.60.
R(-2.70+4.75+2.60)=766.60-423.90+66.50=409.20.
4.65R=409.20, R=88, so T=138 and O=74.
Number of tulips=138, 74 orchids, 88 roses.