If a pair of equations $3x + ky - 9 = 0$ and $x + 2y - 3 = 0$ has infinite solutions,then $k = \ldots$

Solve the following pair of linear equations:
$(a-b)x + (a+b)y = a^2 - 2ab - b^2$
$(a+b)(x+y) = a^2 + b^2$

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method.
The area of a rectangle gets reduced by $9$ square units,if its length is reduced by $5$ units and breadth is increased by $3$ units. If we increase the length by $3$ units and the breadth by $2$ units,the area increases by $67$ square units. Find the dimensions of the rectangle.

Solve the following pair of linear equations: $\frac{25}{x+y} - \frac{7}{x-y} = -2$ and $\frac{15}{x+y} - \frac{7}{x-y} = -4$.

Find the value$(s)$ of $p$ for the pair of equations $2x + 3y - 5 = 0$ and $px - 6y - 8 = 0$ if the system has a unique solution.

The solution set of $x+y-1=0$ and $3x+3y-2=0$ is ...........