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.
$5x - 3y = 11$; $-10x + 6y = -22$

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method.
Yash scored $40$ marks in a test,getting $3$ marks for each right answer and losing $1$ mark for each wrong answer. Had $4$ marks been awarded for each correct answer and $2$ marks been deducted for each incorrect answer,then Yash would have scored $50$ marks. How many questions were there in the test?

The sum of a two-digit number and the number obtained by reversing the digits is $66$. If the digits of the number differ by $2$,find the number. How many such numbers are there?

Solve the following pair of linear equations by the substitution and cross-multiplication methods:
$8x + 5y = 9$
$3x + 2y = 4$

Two rails are represented by the equations $x+2y-4=0$ and $2x+4y-12=0$. Represent this situation geometrically.

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?