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Simultaneous linear equation in two variables, analytical and graphical solutions. Simultaneous linear in equations. Practical problems on linear equations.

Consider the following two sets of equations :
I. 2x - y = 0 and 6x - 3y = 0
II. 3x - 4y = 0 and 12x - 20y = 0

Option:
A. both sets I and II possess unique solutions.
B. Set I possesses unique solution and set II has infinitely many solutions.
C. Set II possesses unique solution and set I possesses infinitely many solutions.
D. None of the sets I and II possesses a unique solution.
Answer: C . Set II possesses unique solution and set I possesses infinitely many solutions.

Justification:

Eqns. in I are 2x - y = 0 & 2x - y = 0
Thus, there is one equation in two variables.
.'. Given equations have an infinite number of solutions.
Eqns. in II are 3x - 4y = 0 & 3x - 5y = 0
Solving these equations, we get x = 0 & y = 0
So, (c) is true.

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