Exercise

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

A part of monthly expenses of a family on milk is fixed for $\mathrm{₹}500$ and the remaining varies with the quantity of milk, taken extra at the rate of $\mathrm{₹}20$ per $\mathrm{kg}$. Taking the quantity of milk required extra as $x \mathrm{k}\mathrm{g}$ and the total expenditure on milk $\mathrm{₹}\mathrm{y}$, write a linear equation for this information and draw its graph.

Two men start from points $A$ and $B$ respectively, $50 \mathrm{k}\mathrm{m}$ apart. One walks from $A$ to $B$ at $x \mathrm{k}\mathrm{m}/\mathrm{h}\mathrm{r}$ and another walks from $B$ to $A$ at $y \mathrm{k}\mathrm{m}/\mathrm{h}\mathrm{r}$. They meet each other after $5$ hours. Write a linear equation for this information and draw its graph.

A fraction becomes $\frac{9}{11}$, if $2$ is added to both the numerator and the denominator. The numerator and denominator of the fraction are $x$ and $y$ respectively. Write a linear equation for this information and draw the graph.

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.

$-4-2x=x+5$

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