(2x+y)a -3yb=4xa +( x-4y +1)b ;(2x+y -4x)a =(3y +x-4y +1)b ;(y -2x)a =(x-y +1)b ;Т.к. a и b не коллинеарны, то:{ y -2x = 0 ; x-y +1 =0 ⇔{ y=2x ; x -2x+1 =0. {y =2*1; x =1.ответ : x =1 , y=2 .**********************Дано: BM/MC =2:1 ; M∈BC ; AO =OM , O∈AM.-------------------------Доказать: BO =(1/2)*BA +(1/3)*BC . BO =BA+AO =BA+AM/2 ;AM = AB+BM =AB +(2/3)BC ⇒ AM/2 =(1/2)*AB +(1/3)*BC.BO =BA+AM/2 =BA+ (1/2)*AB +(1/3)*BC =BA - (1/2)*BA +(1/3)*BC =(1/2)*BA +(1/3)*BC .BO = (1/2)*BA +(1/3)*BC .