Embibe Experts Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: Exercise

If a pair of linear equations $a_{1}x+b_{1}y+c_1=0, a_{2}x+b_{2}y+c_2=0$ in two variables have unique solution then correct relation among the following is

The lines represented by $\mathrm{x} + 2\mathrm{y} – 4 = 0$ and $2\mathrm{x} + 4\mathrm{y} – 12 = 0$are,
 

The value of $k$ for which the system of equations $x+y-4=0$ and $2x+ky=3$, has no solution is 

Express the following statement in the form of simultaneous linear equations and solve them by drawing graph.

The perimeter of rectangular garden of Ajoy is $60 \mathrm{m}$. If its length be $2 \mathrm{m}$ more and breadth be $2 \mathrm{m}$ less than that of the previous, then the area of the garden becomes $24 {\mathrm{m}}^2$ less than the previous area. Determine the length and breadth of the garden.

The sum of squares of two positive numbers is $29$ and their product is $10$. Find the numbers. 

A boat travels upstream  $30$ kilometers and downstream $44$ kilometers in $10$ hours. It also travels up-stream $40$ kilometers and down-stream $55$ kilometers in $13$ hours. Find the velocity of the stream and of the boat in still water.

$2$men and $6$ boys together can do a piece of work in $5$ days. $8$ men and $3$ boys together can do the same work in $3$ days. In how many days $1$ man and $3$ boys together can do the same work?

If the length of a rectangle is increased by $3$ meters and the breadth is decreased by $3$ meters, then the area of the rectangle is decreased by $18$sq. meters. Again, if its length is increased by $3$ meters and the breadth is increased by $3$ meters, then the area of the rectangle is increased by $60$ sq. meters. Find the length and breadth of the rectangle.