Question

2a=4c 6 12b=3c−15 in the system of equations above, a,b, and c are integers. which of the following expressions represents a in terms of b? Option 1: a = 2b - 3 Option 2: a = 3b - 6 Option 3: a = 4b - 6 Option 4: a = 6b - 9

Answer 1

The correct expression representing a in terms of b is Option 1: a = 2b - 3. Therefore,the correct Option is Option 1: a = 2b - 3

Step-by-step explanation:

To find the expression for a in terms of b, we can use the given system of equations:

`\[2a = 4c \quad \text{(1)}\]`

`\[12b = 3c - 15 \quad \text{(2)}\]`

First, let's isolate c in terms of a from equation (1):

`\[a = 2c \quad \text{(3)}\]`

Now, substitute equation (3) into equation (2) to eliminate c:

12b = 3(2a) - 15

12b = 6a - 15

Next, isolate a in terms of b:

`\[a = (12b - 15)/(6)\]`

a = 2b - 3

Comparing this with the given options, the correct expression is Option 1: (a = 2b - 3).

Therefore,the correct Option is Option 1: a = 2b - 3