NCERT Solutions for Chapter: Linear Equations in Two Variables, Exercise 1: Exercise

The soap bottles are available in small and large sizes. A carton with $100$ small and $40$ large bottles weighs $10.8 \mathrm{kg}$ each. What is the mass of the carton with $50$large bottles?

The area of a rectangle gets reduced by $9 \mathrm{sq} \mathrm{units}$, if its length is reduced by $5$ units and breadth is increased by $3$ units. Taking the length and breadth of the rectangle as $x$ and $y$ respectively, write the equation. If we increase the length by $3$ units and breadth by $2$ units, then the area is incraesed by $67 \mathrm{sq} \mathrm{units}$. Another equation so obtained.

If thee times the larger of the two numbers is divided by the smaller one, we get $4$ as quotient and $3$ as remainder. Also, if seven times the smaller number is divided by the larger one, we get $5$ as quotient and $1$ as remainder. Both the equations so obtained is

Give the geometric representation of the following equation (i) in one variable. (ii) in two variables.. And also identify the line parallel to which axis.

$-4-2x=x+5$

Give the geometric representations of following equation (i) in one variable. (ii) in two variables. And also identify the line parallel to which axis.

$2x+7=5x-5$

Angles of a quadrilateral are $5x,4x,6y$ and $3y$. Write a linear equation which satisfies this data. Draw the graph for the same.

If $a{x}^{-2a^2+3}+b{y}^{b^2-3}+2y^{b^2-3}+x^{-2a^2+3}=4$ is a linear equation in $x$ and $y$ then the value of $a+b$ is

If $\frac{3.6}{100}x+\frac{2.2}{100}y=107487.17, \frac{100}{3.6}x+\frac{100}{2.2}y=476233.75$ 

Find x and y