Final answer:
To derive the given system of equations, we start by rearranging the first equation to solve for a. Then substitute this value of a in the second and third equation. Simplify the equations to obtain the derived system.
Step-by-step explanation:
The given system of equations is:
2a + b - 3c = 7
4a - 3b + 2c = 12
a + 2b + c = 5
To derive this system of equations, we start by rearranging the first equation to solve for a:
a = (7 - b + 3c)/2
Next, we substitute this value of a in the second and third equation:
4[(7 - b + 3c)/2] - 3b + 2c = 12
(7 - b + 3c)/2 + 2b + c = 5
Simplifying these equations, we get:
14 - 2b + 6c - 3b + 2c = 24
7 - b + 3c + 4b + 2c = 10
Combining like terms, we have:
-5b + 8c = 10
3b + 5c = 3
Therefore, the derived system of equations is:
-5b + 8c = 10
3b + 5c = 3