Try to form equations for the following statement:

A fruit-basket contains apples and mangoes. The number of fruits is $39$. Another fruit-basket has some mangoes and oranges then find the number of mangoes in the second basket

Draw graphs for the equations $x+y=8$ and $x=3y$, find the solutions.

Write the following statement in the form of equations:

The cricket coach in a school purchased $3$ bats and $6$ balls for $₨.3900$. He bought a bat and two balls from the same shop for $₨.1300$.

Write the following statement in the form of equations:

The sum of two numbers is $16$ and their difference is $8$.

Write the following statement in the form of equations:

The cost of $2 \mathrm{kg}$ apples and $1 \mathrm{kg}$ grapes is $₨.160$ in a fruit shop. In the same shop, the cost of $4 \mathrm{kg}$ apples and $2 \mathrm{kg}$ grapes is $₨.300$.

Write the following statement in the form of equations:

Naresh said to his daughter that seven years ago my age was seven times your age and three years from now I will be three times as old as you.

Write the following statement in the form of equations:

A person travels $90 \mathrm{km}$ by train and taxi to reach his office. The distance travelled by train is twice the distance travelled by taxi.

Solve the above system of equations using different methods. Discuss whether the solutions obtained using the different methods are same or not?
$2x+5y=1$
$2x+3y=3$

Check whether values of $x$ and $y$ given in $\text{'}A\text{'}$ and $\text{'}B\text{'}$ are solutions of given equation:

$\left(A\right) x=2, y=5$,  $\left(B\right) x=-1, y=3$

$x+y=7$