Ans: C<span>
onsistent and Coincident </span>
Explanation:First let me tell you the shortcut to know whether the system is consistent or inconsistent or coincident.
1) Consistent: If system of equations has
at least one solution.
2) Inconsistent: If system of equations has
no solutions.
3) Coincident: If one equation is multiple of the other.
Given Equations:
<span>y=−3x+1 --- (A)
2y=−6x+2 --- (B)
As you can see equation (B) is same as equation (A):
</span>
<span>
=> </span>y=−3x+1 (same as (A))
<span>
It means both the equations lie on top of one another in the graph. Therefore,
there are
infinite solutions of the above system of equations.
Now apply the shortcut! As there are infinite solutions, it means the system is
consistent.
Now let's see the coincident part.
Is one equation a multiple of second equation? YES! As,
equation-B = 2 * {equation-A)
Therefore, the system is coincident as well.
Hence the answer is:
C</span>
onsistent and Coincident <span>
</span>-i