Answer:
the correct answer is d. Consistent System.
Explanation:
To determine the consistency of the system of linear equations:
a - 3b + c = 1
2a - b - 2c = 2
a + 2b - 3c = -1
We can use the method of elimination to solve the system.
First, let's eliminate the variable 'a' from the second and third equations by multiplying the first equation by 2 and subtracting it from the second equation:
2(a - 3b + c) - (2a - b - 2c) = 2(1) - 2
2a - 6b + 2c - 2a + b + 2c = 2 - 2
-5b + 4c = 0 ---- (Equation 4)
Next, let's eliminate the variable 'a' from the third equation by multiplying the first equation by 1 and subtracting it from the third equation:
(a - 3b + c) - (a + 2b - 3c) = 1 - (-1)
a - 3b + c - a - 2b + 3c = 1 + 1
-5b + 4c = 2 ---- (Equation 5)
We can see that Equation 4 and Equation 5 are the same. This means that the system of equations is consistent, as it has the same equation derived from different combinations.Therefore, the answer is d. Consistent System