Question

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10) y = 5x + 2 10x − 2y = 12 Classify the system correctly. A) Inconsistent B) Indeterminate C) Consistent and Dependent D) Consistent and Independent

Answer 1

Option A) Inconsistent is correct

Explanation:

Given equations are
`y=5x+2\hfill (1)`

and
`10x-2y=12\hfill (2)`

Rewritting the equation y=5x+2 as below

5x-y=-2

Now multiplying the above equation into 2 we get

`10x-2y=-4\hfill (3)`

Now subtracting the equations (2) and (3)

10x-2y=12

10x-2y=-4

________

`0\\eq 16`

Therefore the given system of equations has no solution

Therefore it is inconsistent

Therefore given two lines are parallel. Two parallel lines never intersect, so the given system has no solution and is inconsistent.

Option A) Inconsistent is correct