If 15 x + 17 y = 21 and 17 x + 15 y = 11 , then find the value of x + y .

Given equations is 15 x + 17 y = 21 . . . . . . ( i ) and 17 x + 15 y = 11 . . . . . ( i i ) Multiply equation ( i ) by 17 and equation ( i i ) by 15 , we get, 255 x + 289 y = 357 . . . . . . . ( i i i ) 255 x + 225 y = 165 . . . . . . . ( i v ) Subtract equation i v from i i i , we get, ⇒ 255 x + 289 y - 255 x + 225 y = 357 - 165 ⇒ 255 x + 289 y - 255 x - 225 y = 192 ⇒ 64 y = 192 ⇒ y = 3 Substitute the value of y in ( i ) , we get, 15 x + 17 × 3 = 21 ⇒ 15 x = 21 - 51 = - 2 And x + y = − 2 + 3 = 1 Thus, value of x + y is 1 .

EASY

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Write a pair of linear equations in $2$ variables which have infinite solutions.

Important Questions on Pair of Linear Equation in Two Variables

MEDIUM

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

Consider the following pair of linear equations:

(i) $2 x - 3 y = 8, 4 x - 6 y = 9$

(ii) $2 x + 3 y - 9 = 0, 4 x + 6 y - 18 = 0$

HARD

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

The area of a rectangle gets reduced by

80

square units, if its length is reduced by

5

units and the breadth is increased by

2

units. If we increase the length by

10

units and decrease the breadth by

5

units, the area is increased by

50

square units. Find the length and breadth of the rectangle.

EASY

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

x + y = 5

and

x - y = 1

, then find the value of

x

HARD

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

$5$ years ago, I was three times as old as my son. Ten years hence, I will be twice as old as my son. Find my present age and my son's present age.

MEDIUM

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

A father's age is three times the sum of the ages of his two children. After

5

years, his age will be two times the sum of their ages. Find the present age of the father.

EASY

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

Find the value of

x - y

3 x + 2 y = 15, 2 x + 3 y = 10

MEDIUM

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

Solve the following system of linear equations:

$x + y = 3$

$4 x - 3 y = 26$

HARD

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

The denominator of a fraction is $4$ more than twice its numerator. Denominator becomes $12$ times the numerator, if both the numerator and the denominator are reduced by $6,$ find the fraction.

EASY

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

A fraction becomes

\frac{1}{3}

when

2

is subtracted from the numerator and it becomes

\frac{1}{2}

when

1

is subtracted from the denominator. Find the fraction.

EASY

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

The value of

k

for which the system of equations

x + y - 4 = 0

and

2 x + k y = 3

, has no solution is

EASY

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

15 x + 17 y = 21

and

17 x + 15 y = 11

, then find the value of

x + y .

HARD

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

Sita and Geeta are two sisters. If Sita's age is written after Geeta's age a four digit perfect square (number) is obtained. If the same exercise is repeated after

13

years another four digit perfect square (number) will be obtained. What is the sum of the present ages of Sita and Geeta?

MEDIUM

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

Solve the following simultaneous equations:

$4 x + 3 y = 11; 3 x + 4 y = 10$

MEDIUM

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

Solve the pair of equations by reducing them to a pair of linear equations:

$\frac{5}{x - 1} + \frac{1}{y - 2} = 2$

$\frac{6}{x - 1} - \frac{3}{y - 2} = 1$

MEDIUM

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

Out of

555 km

, Vishal travelled certain distance by bus and remaining distance by car. Bus travels with an average speed of

60 km / hr

and the average speed of car is

75 km / hr

. He takes total

8 hours

to complete the journey. Find the distance that Vishal travelled by bus in

km

MEDIUM

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

The sum and the difference of the reciprocals of the ages of Aishwarya and her daughter Aaradhya is

\frac{5}{40}

and

\frac{3}{40}

respectively. Find their ages.

MEDIUM

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

In the following figure, the measures of the angles are given. Solve them by the method of elimination.

Question Image

HARD

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

Solve the following system of linear equations:

$2 x - 3 y = 13$

$7 x - 2 y = 20$

MEDIUM

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

72^{x} \cdot 48^{y} = 6^{x y},

where

x

and

y

are nonzero rational numbers, then

x + y

equals

MEDIUM

Mathematics>Algebra>Pair of Linear Equation in Two Variables>Nature of Solutions of a Pair of Linear Equations

A pen costs Rs.

13

and a note book costs Rs.

17 .

A school spends exactly Rs.

10000

in the year

2017 - 18

to buy

x

pens and

y

note books such that

x

and

y

are as close as possible (i.e.,

|x - y|

is minimum). Next year, in

2018 - 19,

the school spends a little more than Rs.

10000

and buys

y

pens and

x

note books. How much more did the school pay?

Write a pair of linear equations in 2 variables which have infinite solutions.

Important Questions on Pair of Linear Equation in Two Variables

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Write a pair of linear equations in $2$ variables which have infinite solutions.