Pair of Linear ...

On comparing the ratios $$\dfrac {a_1}{a_2}, \dfrac {b_1}{b_2}$$ and $$\dfrac {c_1}{c_2}$$, find out whether the following pairs of linear equations are consistent, or inconsistent.
$$5x - 3y = 11; - 10x + 6y =  22$$

Draw the graphs of the equations $$x - y + 1 = 0$$ and $$3x + 2y - 12 = 0$$. Determine the co-ordinates of the vertices of the triangle formed by these lines and the $$x$$-axis, and shade the triangular region.

Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be." (Isn't this interesting?) What are their present ages? Solve graphically introducing necessary varaibles.

Determine whether the following pairs of linear equations are consistent/inconsistent. 

$$10$$ students of class $$X$$ took part in a Mathematics quiz. If the number of girls is $$4$$ more than the number of boys, find the number of boys and girls who took part in the quiz by graphical method.

On comparing the ratios $$\dfrac {a_1}{a_2}, \dfrac {b_1}{b_2}$$ and $$\dfrac {c_1}{c_2}$$, find out whether the following pairs of linear equations are consistent, or inconsistent.
$$2x - 3y = 8; 4x - 6y = 9$$

Determine whether the following pair of linear equations are consistent/inconsistent.

On comparing the ratios $$\dfrac {a_1}{a_2}, \dfrac {b_1}{b_2}$$ and $$\dfrac {c_1}{c_2}$$, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.
$$6x - 3y + 10 = 0; 2x - y + 9 = 0$$

On comparing the ratios $$\frac {a_1}{a_2}, \frac {b_1}{b_2}$$ and $$\frac {c_1}{c_2}$$, find out whether the lines representing the following pairs of linear equations intersect at a point, or are parallel or coincident.
$$9x + 3y + 12 = 0; 18x + 6y + 24 = 0$$