Question

The pair of linear equations $6x-3y+10=0,2x-y+9=0$ has
(a) one solution
(b) two solutions
(c) many solutions
(d) no solution

Answer 1

(d) no solution
The given equations are of the form a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, where
a₁ = 6, b₁ = - 3, c₁ = 10 and a₂ = 2, b₂ = - 1, c₂ = 9
Since,
$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

$\Rightarrow \frac{6}{2}=\frac{-3}{-1}\ne \frac{10}{9}$

$\Rightarrow \frac{3}{1}=\frac{3}{1}\ne \frac{10}{9}$

Hence, the given system of equations has no solution.