Question

What is the correct classification of the system of equations below?

12x − 3y = 9
y − 4x = -3
A.
parallel
B.
coincident
C.
intersecting

Answer 1

Explanation:

12x − 3y = 9

......(1)

y − 4x = -3 ....(2)

multiply (2) by : -3 you have : -3y +12x =9

same equation so same line : answer B. coincident

Answer 2

Answer: Option B

coincident

Explanation:

We have the following system of equations:

`12x - 3y = 9\\-4x+y = -3`

By definition if a system of linear equations has a solution then the lines intersect.

If the system has infinite solutions then the lines are coincident.

If the system has no solution then the lines are parallel.

To solve the system we multiply the second equation by 3 and add it with the first equation

`12x - 3y = 9`

`-12x+3y = -9`

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`0=0` → The system has infinite solutions. Then the lines are coincident

The answer is the option B.