On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}},$ find out whether the lines representing the following pairs of linear equations intersect at a point,are parallel or coincident:
$6x - 3y + 10 = 0$
$2x - y + 9 = 0$

Solve the pair of equations:
$\frac{2}{x} + \frac{3}{y} = 13$
$\frac{5}{x} - \frac{4}{y} = -2$

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?

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?

Solve the following pair of linear equations by the elimination method and the substitution method:
$x+y=5$ and $2x-3y=4$

Solve the following pair of equations by reducing them to a pair of linear equations:
$\frac{1}{3x+y} + \frac{1}{3x-y} = \frac{3}{4}$
$\frac{1}{2(3x+y)} - \frac{1}{2(3x-y)} = -\frac{1}{8}$