Solve a+b=9; 2b+2c=13; 2a-c=11 unknowly

a = 17/2  and b =1/2 and c = 6

Step-by-step explanation:

the system is :  a+b=9(1)

                        2b+2c=13 (2)

                        2a-c=11 (3)

by (1) and (2) calculate : a and b

by (3) : 2a = 11 +c

so : a = (11+c)/2( *)

by (2) : 2b = 13 -2c

so : b =(13-2c)/2(**)

put the value for a and b by (*) and (**) in (1) :

(11+c)/2. + (13-2c)/2 = 9

(11+c +13-2c)/2 = 9

24-c =18

c = 24-18

c = 6

put this value in (*) and (**)

a = (11+6)/2

a = 17/2

b = (13-12)/2

b =1/2

yoi can verify : 1)     a+b = 9     : 17/2 +1/2 = 18/2 = 9 right

                        2)    2b+2c=13  : 2(1/2)+2(6) =1+12 = 13 right

                        3)    2a-c=11      : 2(17/2)-6 =17-6 = 13right