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

The denominator of a fraction is $6$ more than the numerator. If $1$ is added to the numerator and $3$ is subtracted from the denominator,the fraction becomes $\frac{3}{4}$. Find the fraction.

Places $A$ and $B$ are $90\, km$ apart from each other on a highway. $A$ car starts from $A$ and another from $B$ at the same time. If they move in the same direction,they meet in $9$ hours and if they move in opposite directions,they meet in $\frac{9}{7}$ hours. Find the speeds of the cars.

The numerator of a fraction is $4$ less than the denominator. If the numerator is decreased by $2$ and the denominator is increased by $1,$ then the denominator becomes eight times the numerator. Find the fraction.

Solve the following pair of equations by the method of cross-multiplication:
$x + 2y + 1 = 0$
$2x - 3y - 12 = 0$

Two straight paths are represented by the equations $x-3y=2$ and $-2x+6y=5$. Check whether the paths cross each other or not.