Question

Solve the system of linear equations using linear combination. 3a + 6b = 45 2a – 2b = –12 Which is the solution to the system?

Answer 1

a = b - 6
9b - 18 = 45
b = 7
a = 1

Answer 2

a = 1 and b = 7

Explanation:

System of linear equations is

3a + 6b = 45 ----------------(1)

2a - 2b = -12 ----------------(2)

We have to find the solution to the system we will multiply equation (2) by 3 and add to equation (1).

3a + 6b + 3 (2a - 2b) =45 - 3 × 12

3a + 6b + 6a - 6b = 45 - 36

9a = 9

a = 1

Now we put a = 1 in equation (1)

3 × 1 + 6b = 45

6b = 45 - 3 = 42

b =
`(42)/(6)` = 7

So the solution of the system is a = 1 and b = 7