Pair of Linear ...

A certain two digits number is equal to five times the sum of its digits. If $$9$$ were added to the number, its digits would be reversed. The sum of the digits of the number is:

Solve for $$x$$ and $$y $$
$$\displaystyle \frac{2}{3x+2y}+\frac{3}{3x-2y}=\frac{17}{5};\, \, \frac{5}{3x+2y}+\frac{1}{3x-2y}=2$$

The expression $$ax + b$$ is equal to $$13$$ when $$x$$ is $$5$$ and $$ax + b$$ is equal to $$29$$ when $$x$$ is $$13$$. The value of expression when $$x$$ is $$0.5$$

When one is added to each of two given numbers, their ratio becomes $$3 : 4$$ and when $$5$$ is subtracted from each, the ratio becomes $$7:10$$. The numbers are

Solve graphically: $$5x-6y+30=0$$; $$5x+4y-20=0$$. Also, find the vertices of the triangle formed by the above two lines and $$x$$-axis.

In a zoo there are some pigeons and some rabbits. If the total number of heads is $$300$$ and the total number of legs is $$750$$, then how many pigeons are there?

The total salary of $$15$$ men and $$8$$ women is $$Rs.\ 3050$$. The difference of salaries of $$5$$ women and $$3$$ men is $$Rs.\ 50$$. Find the sum of the salaries of $$3$$ men and $$3$$ women

A students walks from his house at less 4 km per hour and reaches his school late by 5 minutes. If his speed has been increase by 5 km per hour then he would have reached 10 minutes early. The distance of the school from his house is

Solve for $$x$$ and $$y$$, if $$2x+ 3y= 8$$ and $$x+2y=5$$.

The sum of the digits of a two-digit number is $$5$$. The digit obtained by increasing the digit in tens' place by unity is one-eighth of the number. Then the number is