Question

Show that the system of equations
6x + 5y = 11,
9x + 152 y = 21
has no solution.

Answer 1

The given system of equations can be written as
6x + 5y – 11 = 0                          ….(i)
`⇒9x + 15/2 y - 21 = 0`                   …(ii)
This system is of the form
`a_1x+b_1y+c_1 = 0`
`a_2x+b_2y+c_2 = 0`
Here, `a_1 = 6, b_1= 5, c_1= -11 and a_2 = 9, b_2= 15/2 , c_2= -21`
Now,
`(a_1)/(a_2) = 6/9 = 2/3`
`(b_1)/(b_2) = 5/(15/2) = 2/3`
`(c_1)/(c_2) = (−11)/(−21) = 11/21`
Thus, `(a_1)/(a_2) = (b_1)/(b_2 )≠ (c_1)/(c_2)`, therefore the given system has no solution.