Pair of Linear ...

Solve the following system of linear equations graphically: $$2x + y = 6, x - 2y + 2 = 0$$. Find the vertices of the triangle formed by the above two lines and the $$x$$-axis. Also find the area of the triangle.

Rs. 58 is divided among 150 children such that each girl gets 25p and each boy get 50p. How many boys are there ?

Solve the following pair of equations by reducing them to a pair of linear equations:

Two years ago, a father was five times as old as his son. Two years later, his age will be $$8$$ more than $$3$$ times the age of the son. Find the present age of father.

Solve the following pair of equations by reducing them to a pair of linear equations:

Solve graphically the following system of linear equations:
$$3x + y+ 1 = 0$$
$$2x - 3y + 8 = 0$$

Albert buys $$4$$ horses and $$9$$ cows for Rs. $$13400$$. If he sells the horses at $$10\%$$ profit and the cows at $$20\%$$ profit, then he earns a total profit of Rs. $$1880$$. The cost of a horse is

Mr. Joshi has $$430$$ cabbage-plants which he wants to plant out. Some $$25$$ to a row and the rest $$20$$ to a row. If there are to be $$18$$ rows in all how many rows of $$25$$ will there be?

The difference between two numbers is $$ 7$$  and their sum is $$35$$. What will be their product?

For what value of $$k$$ does the system of equations $$\displaystyle 2x+ky=11\:and\:5x-7y=5$$ has no solution?