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If $x = a, y = b$ is the solution of the equation $x - y = 2$ and $x + y = 4$ then the values of $a$ and $b$ are respectively

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Important Questions on Linear Equations in Two Variables

HARD

Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

The sum of the digits of a two-digit number is

10

. When the digits are reversed, the number decreases by

54

. Find the changed number:

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Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

How many solutions will a pair of linear equations have, if the equations are

4 x + 5 y - 6 = 0

and

16 x + 20 y + 20 = 0

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Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

Find the value/values of x for the given equation.

$2^{(2 x + 3)} - 17 = 9 (2^{x} - 2)$

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

The sum of four consecutive even numbers is greater than sum of three consecutive odd numbers by

81

. If the sum of least odd and even number is

59

, then find the sum of the largest odd and even numbers.

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

The cost price of

3

exam pads and

2

pencils is

₹ 96 . 4

exam pads and

3

pencils cost

₹ 134

. Find total cost (in

₹

) of an exam pad and that of a pencil.

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

A number exceeds its

\frac{1}{9}

64

. What is the number?

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

Find the value of

x

after solving the following equation.

0.12 \times (5 x - 4) = 0.5 x + 0.8

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Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

The point of the intersection of the graph of the equations

3 x - 5 y = 19

and

3 y - 7 x + 1 = 0

P (α, β)

. What is the value of

(3 α - β)

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Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

A zoo has few number of penguins and polar bears. The total number of heads of both of them is

60

and total number of their feet is

160

. How many polar bears are there in the zoo.

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

The population of Patna city is $96000$ , the decreasing rate of population is $800$ per year. Population of Patliputra is $68000$ , the increasing rate of population is $1200$ per year. In how many years will the population of both places be equal?

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

4

5^{t h s}

of an estate is worth Rs. 16800, then the value of

3

7^{t h s}

of the estate is

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Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

P and Q are two examination halls. If

10

examinees are sent from P into Q, the number of examinees becomes equal in both the halls. If

20

examinees are transferred from Q into P, the number of examinees becomes double in P in comparison with Q. What is the number of examinees in each P and Q separately ?

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Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

x, y, z

are three integers such that

x + y = 8

y + z = 13

and

z + x = 17

, then the value of

\frac{x^{2}}{y z}

is:

HARD

Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

3

chairs and

2

tables cost

R s . 700

and

5

chairs and

3

tables cost

R s . 1100

. What is the cost of

1

chair and

2

tables?

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Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

The graph of the equation

5 x - 2 y + 1 = 0

and

4 y - 3 x + 5 = 0,

intersect at the point

P (α, β)

. What is the value of

(2 α - 3 β)

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

While tabulation of marks scored in an examination by the students of a class, by mistake the marks scored by one student got recorded as

93

in place of

63

, and thereby the average marks increased by

0.5

. What was the number of students in the class?

EASY

Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

The graph of the equations

2 x + 3 y = 11

and

x - 2 y + 12 = 0

intersects at

P (x_{1}, y_{1})

and the graph of the equation

x - 2 y + 12 = 0

intersects the

x -

axis at

Q (x_{2}, y_{2})

. What is the value of

(x_{1} - x_{2} + y_{1} + y_{2})

MEDIUM

Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

Find the number of solutions of a pair of linear equation

4 x - 9 y + 13 = 0

and

2 x + 3 y - 13 = 0

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Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

x

and

y

are positive integers and

\frac{3 x}{y} = 4,

then find the minimum value of

(3 x + 4 y)

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Mathematics>Algebra>Linear Equations in Two Variables>Algebraic Methods of Solving a Pair of Linear Equations

A number of two digits is equal to '

k

' times to the sum of these digits. If the places of these digits are mutually exchanged. the newly formed number is equal to the sum of these digits multiplied by which one of the following options ?

If x=a, y=b is the solution of the equation x-y=2 and x+y=4 then the values of a and b are respectively

Important Questions on Linear Equations in Two Variables

Learn and Prepare for any exam you want !

If $x = a, y = b$ is the solution of the equation $x - y = 2$ and $x + y = 4$ then the values of $a$ and $b$ are respectively