Check whether the following equations are consistent or inconsistent. Solve them graphically:

$$\begin{gathered} 2x+y-6=0 \\ 4x-2y-4=0 \end{gathered}$$

Check whether the following equations are consistent or inconsistent. Solve them graphically:

$$\begin{gathered} 2x-2y-2=0 \\ 4x-4y-5=0 \end{gathered}$$

Neha went to a 'sale' to purchase some pants and skirts. When her friend asked her how many of each she had bought, she answered, "the number of skirts are two less than twice the number of pants purchased and the number of skirts is four less than four times the number of pants purchased." 

Help her friend to find how many pants and skirts Neha bought.

$10$ students of Class-$\mathrm{X}$ took part in a mathematics quiz. If the number of girls is $4$ more than the number of boys then, find the number of boys and the number of girls who took part in the quiz.

$5$ 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.