The cost of $2 \mathrm{k}\mathrm{g}$ of apples and $1 \mathrm{k}\mathrm{g}$ of grapes on a day was found to be $\mathbf{₹}160$. After a month, the cost of $4 \mathrm{k}\mathrm{g}$ of apples and $2 \mathrm{k}\mathrm{g}$ of grapes is $\mathbf{₹}300$. Represent the situation algebraically and geometrically.

Form the pair of linear equations in the following problem and find their solution graphically.

$10$ 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.

Form the pair of linear equations in the following problems and find their solutions graphically.

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, are parallel or coincident:

$5x-4y+8=0$

$7x+6y-9=0$

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, are parallel or coincident.
$9x+3y+12=0$
$18x+6y+24=0$

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, are parallel or coincident.

 $6x-3y+10=0$ and $2x-y+9=0$

On comparing the ratios $\frac{a_1}{a_2},\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the following pair of linear equations are consistent, or inconsistent.

$3x+2y=5; 2x-3y=7$

On comparing the ratios $\frac{a_1}{a_2},\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the following pair of linear equations are consistent, or inconsistent.

$2\mathrm{x}-3\mathrm{y}=8;$    $4x-6y=9$

On comparing the ratios $\frac{a_1}{a_2},\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the following pair of linear equations are consistent, or inconsistent.