Solve the following pair of linear equations by the method of substitution: $8x - 3y = 1$ and $34x - 3y = 14$.

$A$ shopkeeper sells a saree at $8 \%$ profit and a sweater at $10 \%$ discount,thereby,getting a sum of $Rs. 1008$. If she had sold the saree at $10 \%$ profit and the sweater at $8 \%$ discount,she would have got $Rs. 1028$. Find the cost price of the saree and the list price (price before discount) of the sweater (in $Rs.$).

The solution of the pair of equations $x + 2y = 5$ and $3x + 5y = 13$ is ...........

Solve the following pair of equations by the method of cross multiplication:
$x + y - (a + b) = 0$
$ax - by - (a^2 - b^2) = 0$

Devarshi got thrice the marks as obtained by Maharshi in the annual examination of mathematics of standard $10$. The sum of the marks obtained by them was $150$. Represent this situation as a pair of linear equations in two variables.

Write a pair of linear equations which has the unique solution $x = -1, y = 3$. How many such pairs can you write?