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

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.

The total price of $9$ horses and $7$ cows is $₹3000$ and at the same rate , the total price of 6 horses and $13$ cows is $₹3000$. What will be the total price of $5$ horses and $3$ cows at the same rate?

$2$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 a man sells $7$ horses and buys $9$ cows his purse increases by $₹176$,  but if he sells $13$ cows and buys $9$ horses his purse decreases by $₹182$. Find the cost of cow.

If the simultaneous linear equations in the two variables $x+ry=r$ and $x+{(r-2)}^{2}y=2$ have no solutions then, find the values of $r$.

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

5 times of the greater one of two numbers is 2 more than 8 times of the smaller one. Again 2 times of the smaller one is 10 more than the greater one. Find the two numbers.

Solve simultaneous linear equations in two variables by the method of elimination.

$41x+53y=135, 53x+41y=147$