Question

The pair of equations x +2y=5 & 3x+12y =10 has
(a unique solution, no solution, more than 2 solutions, infinitely many
Solutions )

Answer 1

Answer:

it has a unique solution.

here, a1=1. b1=2. c1= -5

a2=3. b2=12. c2=-10

So ,

a1/a2=1/3

b1/b2=2/12=1/6

c1/c2= -5/-10=1/2

here ,

a1/a2 is not equal to b1/b2

Thus , it has a unique solution

Answer 2

Answer: The pair of linear equations has only one solution i.e. Unique solution.

Given the pair of equations

Equation 1 : x + 2y = 5

Equation 2 : 3x + 12y = 10

x + 2y - 5 = 0 and 3x + 12y - 10 = 0

It is to be found that whether the pair of equations has a unique solution, no solution or infinitely many solutions.

Number of solutions depend upon the relationship between the coefficients as,

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0 are two linear equations then the relationship to be checked between,

a1/a2 , b1/b2 & c1/c2

As, 1/3 ≠ 2/12

1/3 ≠ 1/6

The pair of linear equations has one and only one solution i.e. unique solution.

To conclude in one sentence, the pair of linear equations has unique solution.

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