Graphically, find the number of solution for the following pair of linear equations in two variables:
6x – 3y + 10 = 0
2x – y + 9 = 0

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Solution

The first equation is
$6 x - 3 y + 10 = 0$
$\Rightarrow 2 x - y + \frac{10}{3} = 0$
$y = 2 x + \frac{10}{3}$

$\begin{matrix} x & 0 & - \frac{5}{3} y & \frac{10}{3} & 0 P o i n t s & A & B \end{matrix} A n d t a b l e f o r 2 x - y + 9 = 0 \begin{matrix} x & 0 & - \frac{9}{2} Y = 2 x + 9 & 9 & 0 P o i n t s & C & D \end{matrix}$

Since, the given pair of linear equations in two variables represents two parallel lines.
hence, no solution.

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