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

Answer: 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 = 13 ... right