The pair of equations `x + 2y + 5 = 0` and ` -3x - 6y + 1 = 0` has

Options

A. a unique solution
B. exactly two solutions
C. infinitely many solutions
D. no solution

Answer

D

Explanation

Given, equations are `x+2y+5 = 0` and `-3x-6y+1 = 0`
Here, `" " a_(1) = 1, b_(1) = 2, c_(1) = 5` and `a_(2) = -3, b_(2) = -6, c_(2) = 1`
`:. " " (a_(1))/(a_(2))=-(1)/(3), (b_(1))/(b_(2))=-(2)/(6) = -(1)/(3)`,
`" " (c_(1))/(c_(2))=(5)/(1)`
`:. " " (a_(1))/(a_(2))=(b_(1))/(b_(2))!= (c_(1))/(c_(2))`
Hence , the pair of equations has no solution.