Solve the system

Question

Solve the system, if possible. (If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)

4a − 3b = 1
6a − 8c = 1
2b − 4c = 0

Answer 1

I don't know how to write a matrix on here so we'll have to do this old school style:

 

4a-3b=1 (eqn 1)

6a- 8c=1 (eqn 2)

2b-4c=0 (eqn 3)

 

Let's look at eqn 3: 2b-4c=0. We can rewrite it as 2b=4c, and further simplify it to b=2c. Now let's convert eqn 1 to make it more similar to eqn 2:

 

4a-3b=1 becomes 3a-3(2c)=1. Simplified, the new equation 1 is 4a-6c=1. Now, let's solve for a in both the new eqn 1 and eqn 2:

 

eqn 1: 4a= 1 + 6c  ==> a= (1/4)*(1+3c)=(1/4) + 1.5c    

eqn 2: 6a= 1 +8c  ==> a= (1/6)*(1+8c)=(1/6)+(8/6)c

 

The values for a are contradicting each other, therefore you have an inconsistent system