Question

1. Solve the system by the linear combination method. Show all work carefully.

2.Check your answer.
a - 2b = 2
a + b - 2(b+3)

Answer 1

a + b - 2(b+3)=0
a + b - 2b - 6=0
a - b - 6= 0

a - 2b = 2
a - b = 6
–––––––
-b = -4
b = 4

Put this "b" value into the 1st equation:
a - 2b = 2
a - 8 = 2
a = 10


Check this :
10 – 8 = 2 .......... correct
10 + 4 = 2(4 + 3) .......... correct

Answer 2

a - 2b = 2 . . . (1)
a + b = 2(b + 3)
a + b = 2b + 3
a - b = 3 . . . (2)

(1) - (2) => -b = -1 => b = 1

From (2): a - 1 = 3 => a = 3 + 1 = 4
Therefore, a = 4 and b = 1