Question

What type of system is the following set of equations?

( -3x + y = -2

( y - 4 = -6x


A. consistent, independent

B. consistent, dependent

C. inconsistent

D. independent

Answer 1

A. CONSISTENT; INDEPENDENT

Explanation:

We say a system of equations is inconsistent when the system has no solutions. In two variable case, the lines are parallel.

The system of equations is consistent when the system has solutions. The solutions could be unique or there could be infinite of them.

When the solution is unique, we call it an Independent Consistent system.

If the equations are constant multiples of each other then they have infinite solutions and such a system is called as Consistent Dependent system.

The given equations are:

`$ - 3x + y = -2 \hspace{15mm} ....(1) $`

`$ 6x + y = 4 \hspace{15mm}.....(2)$`

Solving for
`$ x $` and
`$ y $`, we have:

`$ x = (2)/(3) $` and
`$ y = 0 $`.

We see that the system has a unique solution. So it should be Consistent and Independent.