The pair of equations $y=0$ and $y=-7$ has

Solve the following pair of equations by the method of cross multiplication:
$x + y - (a + b) = 0$
$ax - by - (a^2 - b^2) = 0$

The sum of a two-digit number and the number obtained by interchanging its digits is $110$. If the number obtained by subtracting $10$ from the original number exceeds five times the sum of the digits of the original number by $4$,then find the original number.

Solve the following pairs of equations by the cross-multiplication method:
$0.5x + 0.3y = 0.1$
$0.6x + 0.3y = 0.3$

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.

Solve the following pair of equations by reducing them to a pair of linear equations:
$\frac{1}{2x} + \frac{1}{3y} = 2$
$\frac{1}{3x} + \frac{1}{2y} = \frac{13}{6}$