Solve algebraically: 6a+b = 16 and 5a - 2b = 19

6a + b = 16 (1)

5a - 2b = 19 (2)

(1) x 2: 12a + 2b =32

(1) + (2): 12a + 2b + 5a - 2b = 32 + 19 = 51

17a = 51

a = 51 / 17 = 3

Substitue a = 3 back into (1): (6 x 3) + b = 16

18 + b = 16

b = 16 - 18 = - 2

Substitute a = 3 and b = -2 into (2) to check

(5 x 3) - (2 x - 2) = 19

15 - - 4 = 15 + 4 = 19