Is the pair of equations $x+2y-3=0$ and $6y+3x-9=0$ consistent? Justify your answer.

$6$ students of class $X$ took part in the Ramanujan Competitive Examination. The number of girl participants is $2$ less than the number of boy participants. Find the number of girls and the number of boys who took part in the examination using a graph.

The graph of the equation $\ldots \ldots \ldots \ldots$ is parallel to the $Y$-axis.

Solve the following pair of linear equations in two variables using a graph: $x + y = 8$ and $x - y = 2$.

$A$ shopkeeper sells a saree at $8 \%$ profit and a sweater at $10 \%$ discount,thereby,getting a sum of $Rs. 1008$. If she had sold the saree at $10 \%$ profit and the sweater at $8 \%$ discount,she would have got $Rs. 1028$. Find the cost price of the saree and the list price (price before discount) of the sweater (in $Rs.$).

Solve the following pairs of linear equations: $\frac{2}{x} + \frac{3}{y} = \frac{9}{xy}, \quad \frac{4}{x} + \frac{9}{y} = \frac{21}{xy} \quad (x \neq 0, y \neq 0)$