Question

this system of linear equations are a-3b+c=1 2a-b-2c=2 a+2b-3c=-1 Select one: a. Inconsistent System b. infinite number of solutions C. one solution d. Consistent System

Answer 1

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