Question

2a + 3b – 2c = 18

5a + 6b + c = 21
4b – 2c - 6 = 0
Solve if inconsistent or equations are dependent state as is."
a) Inconsistent
b) Dependent
c) Consistent

Answer 1

The given system of equations is inconsistent, as it leads to a contradiction. Therefore, the answer is option (a) Inconsistent.

Step-by-step explanation:

The given equations are:

2a + 3b – 2c = 18

5a + 6b + c = 21

4b – 2c - 6 = 0

To solve the system of equations, we can use the method of substitution or elimination. Let's use elimination:

Multiplying the first equation by 2 and the second equation by 4, we get:

4a + 6b - 4c = 36

20a + 24b + 4c = 84

Adding these two equations, we eliminate the variable c:

24a + 30b = 120

Multiplying the third equation by 3 and adding it to the previous equation, we eliminate the variable b:

24a + 30b + 12c = 36

27a + 42c = 156

Finally, we can solve this system of equations using any method. From the equations above, we can see that it leads to a contradiction, indicating that the system is inconsistent. Therefore, the answer is option (a) Inconsistent.