MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.5>Q 27

MEDIUM

10th CBSE

IMPORTANT

Earn 100

For what value of $α$ , the system of equations will have no solution?
$α x + 3 y = α - 3$
$12 x + α y = α$

Important Questions on Pair of Linear Equations in Two Variables

EASY

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.5>Q 28

Find the value of

k

for which the system has a unique solution:

k x + 2 y = 5

3 x + y = 1

EASY

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.5>Q 28

Find the value of $k$ for which the system has no solution.

$k x + 2 y = 5$

$3 x + y = 1$

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.5>Q 29

Prove that there is a value of

c (\neq 0)

for which the system has infinitely many solutions. Find this value.

6 x + 3 y = c - 3

12 x + c y = c

EASY

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.5>Q 30

What should not be the value of $k$ if the following system of linear equations has a unique solution. [Answer as an improper fraction]

$2 x + k y = 1$

$3 x - 5 y = 7$

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.5>Q 30

Find the values of

k

for which the system will have no solution. Is there a value of

k

for which the system has infinitely many solutions?

2 x + k y = 1

3 x - 5 y = 7

EASY

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.5>Q 31

For what value of

k

, the following system of equations will represent the coincident lines?

x + 2 y + 7 = 0

2 x + k y + 14 = 0

EASY

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.5>Q 32

Obtain the condition for the following system of linear equations to have a unique solution:

a x + b y = c

l x + m y = n

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.5>Q 33

Determine the values of

a

and

b

so that the following system of linear equations have infinitely many solutions :

(2 a - 1) x + 3 y - 5 = 0

3 x + (b - 1) y - 2 = 0