Question

The pair of equations 3x – 5y = 7 and – 6x + 10y = 7 have ​

Answer 1

The pair of linear equations 3x - 5y = 7 and 6x - 10y = 7 has no solution. There are basically three types of solutions for the pair of linear equations, i.e; Unique solution, Infinitely many solutions and no solution.

Answer 2

Given :  pair of equations 3x – 5y = 7 and – 6x + 10y = 7

To Find : Number of the solutions

Solution:

Pair of linear equations

a₁x  +  b₁y + c₁  =  0

a₂x  +  b₂y + c₂  =  0

Consistent

if a₁/a₂ ≠ b₁/b₂   (unique solution  and lines intersects each others)

  a₁/a₂ = b₁/b₂ = c₁/c₂   (infinite solutions and line coincide each other )

Inconsistent

if  a₁/a₂ = b₁/b₂ ≠  c₁/c₂  ( No solution , lines are parallel to each other)

  3x – 5y = 7  

– 6x + 10y = 7

3/-6  = -5/10   ≠ 7/7

-1/2 = -1/2  ≠ 1

Hence No solution

Lines are parallel

The pair of equations 3x – 5y = 7 and – 6x + 10y = 7 have ​ NO SOLUTION

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