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.

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:
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$

Formulate the following problems as a pair of equations,and hence find their solutions:
$2$ women and $5$ men can together finish an embroidery work in $4$ days,while $3$ women and $6$ men can finish it in $3$ days. Find the time taken by $1$ woman alone to finish the work,and also that taken by $1$ man alone.

For which values of $a$ and $b$ does the following pair of linear equations have an infinite number of solutions?
$2x + 3y = 7$
$(a-b)x + (a+b)y = 3a + b - 2$

One says,"Give me a hundred,friend! $I$ shall then become twice as rich as you". The other replies,"If you give me ten,$I$ shall be six times as rich as you". Tell me what is the amount of their (respective) capital?

Draw the graphs of the equations $5x - y = 5$ and $3x - y = 3$. Determine the coordinates of the vertices of the triangle formed by these lines and the $y$-axis.