$5$ 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.

Half the perimeter of a rectangular garden is $36 \mathrm{m}$. If the length is $4 \mathrm{m}$ more than its width. Find the dimensions of the garden.

We have a linear equation $2x+3y-8=0$. Write another linear equation in two variables $x$ and $y$ such that the geometrical representation of the pair so formed is intersecting lines.

Now, write two more linear equations so that one forms a pair of parallel lines and the second forms coincident line with the given equation.

The area of a rectangle gets reduced by $80 \mathrm{sq}$ units if its length is reduced by $5$ units and breadth is increased by $2$ units. If we increase the length by $10$ units and decrease the breadth by $5$ units, the area will increase by $50 \mathrm{sq}$ units. Find the length and breadth of the rectangle.

In a class, if three students sit on each bench, one student will be left. If four students sit on each bench, one bench will be left. Find the number of students and the number of benches in that class.

Solve the following pair of equations by using the substitution method.

$3x-5y=-1$

$x-y=-1$

Solve the following pair of equations by using the substitution method.

$x+2y=-1$

$2x-3y=12$

Solve the following pair of equations by using the substitution method.

$2x+3y=9$

$3x+4y=5$

Solve the following pair of equations by using the substitution method.

$x+\frac{6}{y}=6$

$3x-\frac{8}{y}=5$