Assam Board Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 5: Exercise 3.5

Check whether the following pair of linear equation has a unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method.

$2x+y=5 , 3x+2y=8$

Check whether the following pair of linear equation has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method.

$3x-5y=20 , 6x-10y=40$

Does the following pair of linear equation have a unique solution, no solution, or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.

$x-3y-7=0$ , $3x-3y-15=0$

For which value of $k$ will the following pair of linear equations have no solution?
$3x+y=1$
$\left(2k-1\right)x+\left(k-1\right)y=2k+1$

Find the pair of linear equations in the problem and find the solution (if it exists) by any algebraic method:

A fraction becomes $\frac{1}{3}$ when $1$ is subtracted from the numerator and it becomes $\frac{1}{4}$ when $8$ is added to its denominator. Find the fraction.

Yash scored $40$ marks in a test, getting $3$ marks for each right answer and losing $1$ marks for each wrong answer. If $4$ marks had been awarded for each correct answer and $2$ marks been deducted for each incorrect answer, then Yash would have scored $50$ marks. How many questions were there in the test?

Form the pair of linear equation in the following problem and find its solution(if they exist) by any algebraic method:

Places $\mathrm{A}$ and $\mathrm{B}$ are $100\mathrm{}\mathrm{k}\mathrm{m}$ apart on a highway. One car starts from $\mathrm{A}$ and another from $\mathrm{B}$ at the same time. If the cars travel in the same direction at different speeds, they meet in $5$ hours. If they travel towards each other, they meet in $1$ hour. What are the speeds of the two cars?

Form the pair of linear equations in the following problem and find their solutions (if they exist) by any algebraic method:

 The area of a rectangle gets reduced by $9$ square units, if its length is reduced by $5$ units and breadth is increased by $3$ units. If we increase the length by $3$ units and the breadth by $2$ units, the area increases by $67$ square units. Find the dimensions of the rectangle.