The equations 3x - 4y = 5 and 12x - 16y = 20 have : - Linear Equations - Algebra - Mathematics quest

The equations 3x - 4y = 5 and 12x - 16y = 20 have :

A. no common solution.

B. exactly one common solution.

C. exactly two common solutions.

D. more than two common solutions.

E. None of the above

Answer: D. more than two common solutions.

The given equations are 3x - 4y = 5 and 12x - 6y = 20.
So, (12x - 16y = 20) = { 4(3x - 4y) = 4(5)} = 3x - 4y = 5.
So, The given equations are 3x - 4y = 5 and 3x - 4y = 5.
Thus, there is one equation in two variables.
So, the given equations have an infinite number of solutions.
Hence, the answer is (d).

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