Solve the following system of equations for the given variables.

$x+y=7$,

$x-y=-1$

Solve the following system of equations for the given variables.

$2x+y=8$,

$x-2y=-1$

Solve the following system of equations for the given variables.

$4x+3y=5$,

$2x-y=2$

Solve the following system of equations for the given variables.

$\sqrt{7}x+\sqrt{11}y=0$,

$\sqrt{3}x-\sqrt{5}y=0$

The cost of $15 \mathrm{kg}$ tea and $17 \mathrm{kg}$ coffee is $₹183$ and the cost of $25 \mathrm{kg}$ tea and $13 \mathrm{kg}$ coffee is $₹213$. If the cost of $7 \mathrm{kg}$ tea and $1 \mathrm{kg}$ coffee is $₹k$, then find the value of $k$. (Express answer up to two decimal places)

A person owns some pigeons and cows. The number of legs of these animals is $180$ and the total number of eyes is $120$. How many cows and pigeons does the person own?

A bag has $50 \mathrm{paisa}$ and $25 \mathrm{paisa}$ coins. The total number of coins is $94$ and their value is $₹29.75$. Find the number of $50 \mathrm{paisa}$ and $25 \mathrm{paisa}$ coins.

The sum of two numbers is $25$. The sum of their reciprocals is $\frac{1}{4}$. Find the two numbers.

The difference of two numbers is $14$ and the difference in their squares is $448$. Find the numbers.