The general form of a linear equation in two variables is .......... (where,$a^{2}+b^{2} \neq 0$).

The pair of equations $ax - y = 5$ and $4x - 2y = 10$ has an infinite number of solutions. Then $a = \ldots$

For what value of $k$ will the following pair of linear equations have infinitely many solutions?
$kx + 3y - (k - 3) = 0$
$12x + ky - k = 0$

$x$ years ago,the sum of the ages of a mother,father,and two children was $y$ years. What will be the sum of their ages after $z$ years?

The solution set of a pair of equations $3x + 3y - 3 = 0$ and $5x + 5y - 5 = 0$ is $\ldots \ldots \ldots \ldots$

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}},$ find out whether the following pair of linear equations are consistent or inconsistent.
$3x + 2y = 5; \quad 2x - 3y = 7$