$x$ 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?

Do the following equations represent a pair of coincident lines? Justify your answer.
$-2x - 3y = 1$
$6y + 4x = -2$

The standard form of $2x = 5y$ is............

$8$ men and $12$ women can finish a piece of work in $10$ days. While $6$ men and $8$ women can finish it in $14$ days. Find the time taken by one man alone and that by one woman alone to finish the work.

In the pair of equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,if $\ldots \ldots \ldots \ldots$ then there is no solution (the solution set is an empty set).

The ratio of incomes of two persons is $9:7$ and the ratio of their expenditures is $4:3$. If each of them manages to save ₹ $2000$ per month,find their monthly incomes.