Pair of Linear ...

A man gets Rs. 100 per day if he works, but he is  fined by Rs. 10 per day if he is absent. In the whole month of April he received Rs. 1900 only. How many days did he work ? 

If $$12x\, +\, 13y\, =\, 29\, and\, 13x\, +\, 12y\, =\, 21,$$ find $$x\, +\, y$$.

Solve the following pair of equations. $$25x-24y=197; \, \,  24x-25y=195$$

Solve graphically:
$$\displaystyle 2x-3y=7 $$ and $$\displaystyle 5x+y=9$$

Solve the following simultaneous equation :
$$ax\, +\, by\, =\, 5$$ and $$\, bx\, +\, ay\, =\, 3,$$ where $$a$$ and $$b$$ are constants.

A triangle is formed by the straight lines: $$\displaystyle x + 2y - 3 = 0, 3x - 2y + 7 = 0$$ and $$\displaystyle y + 1 = 0$$. 

Solvw the following pair of linear equations: