Q.

Is it true that the equations 3x– 4= 12 and 4+ 3= 12 have a unique solution?


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a

True

b

False 

answer is B.

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Detailed Solution

Given equations are 3x– 4= 12 and 4+ 3= 12.
We know that a pair of linear equations where a,b0,   has a unique solution if, a 1 a 2 b 1 b 2  .
And, has no solution if, a 1 a 2 = b 1 b 2 c 1 c 2  .
From the linear equation 3x4y=12 and 3x+4y=12,   we get the values as, a 1 =3, b 1 =4, c 1 =12 and  a 2 =3, b 2 =4, c 2 =12.   The ratios of the coefficients are,
a 1 a 2 = 3 3 a 1 a 2 =1, b 1 b 2 = 4 4 b 1 b 2 =1, c 1 c 2 = 12 12 c 1 c 2 =1   Since, these values satisfy the relation a 1 a 2 = b 1 b 2 c 1 c 2 .  
So, the given statement is false.
The correct statement is, the pair of linear equations x+3y=11 and 2(2x+6y)=22   is inconsistent and has no solutions.
Hence, the correct option is 2.
 
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Is it true that the equations –3x– 4y = 12 and 4y + 3x = 12 have a unique solution?