Form the pair of linear equations for the following problem and find their solution by the substitution method.
The difference between two numbers is $26$ and one number is three times the other. Find the numbers.

Which of the following pairs of linear equations are consistent/inconsistent? If consistent,obtain the solution graphically: $x-y=8, 3x-3y=16$.

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 are coincident:
$5x - 4y + 8 = 0$
$7x + 6y - 9 = 0$

$A$ train covered a certain distance at a uniform speed. If the train would have been $10\, km/h$ faster,it would have taken $2\, hours$ less than the scheduled time. And,if the train were slower by $10\, km/h$,it would have taken $3\, hours$ more than the scheduled time. Find the distance covered by the train. (in $, km$)

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?

Form the pair of linear equations in the following problems,and find their solutions graphically.
$5$ pencils and $7$ pens together cost ₹ $50$,whereas $7$ pencils and $5$ pens together cost ₹ $46$. Find the cost of one pencil and that of one pen.