For a pair of equations $5x - 4y = 1$ and $10x = 8y + 2$,in usual notations $a_{1}b_{2} - a_{2}b_{1} = \dots$

Solve the following pairs of equations by the cross-multiplication method:
$4x + 6y = 11$
$5x - 8y = 6$

Use the method of elimination to find the solution of the following pair of linear equations: $0.4 x + 0.3 y = 1.7, 0.7 x - 0.2 y = 0.8$

Prashant purchases $2$ mobiles and $3$ memory cards for Rs. $6500$. The cost of one mobile and one memory card is Rs. $2950$. Represent this as a pair of linear equations in two variables.

The value of $c$ for which the pair of equations $cx - y = 2$ and $6x - 2y = 3$ will have infinitely many solutions is

Rajvansh invested some amount at the rate of $12 \%$ simple interest and some amount at the rate of $10 \%$ simple interest. He received a yearly interest of Rs. $130$. However,if he had interchanged the amounts invested,he would have received Rs. $4$ more as interest. How much amount did he invest at each rate?