R. D. Sharma Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: EXERCISE 3.1

Gloria is walking along the path joining $(-2, 3)$and $(2, -2)$, while Suresh is walking along the path joining $(0, 5)$ and $(4, 0).$Represent this situation 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 coincide.
$$\begin{gathered} 5x + 4y + 8 = 0 \\ 7x + 6y - 9 = 0 \end{gathered}$$

On comparing the ratios $\frac{a_1}{a_2}$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide :
$9x + 3y + 12 = 0$
$18x + 6y + 24 = 0$

On comparing the ratios $\frac{a_1}{a_2}$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide :
$$\begin{gathered} 6x - 3y + 10 = 0 \\ 2x - y + 9 = 0 \end{gathered}$$

Given linear equation is $2x+3y-8=0$. Write another linear equation in two variables such that the geometrical representation of the pair so formed are intersecting lines.

Given the linear equation $2x+3y-8=0$, write another linear equation in two variables such that the geometrical representation of the pair so formed is parallel lines.

Given the linear equation $2x+3y-8=0$, write another linear equation in two variables such that the geometrical representation of the pair so formed is coincident lines.

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