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$0 x + 0 y + k = 0$ , $(k \neq 0)$ is a linear equation.

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Important Questions on Simultaneous Equations

EASY

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

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.

MEDIUM

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

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)

MEDIUM

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

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.

HARD

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

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.

MEDIUM

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

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

HARD

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

Solve the following system of linear equations:

$2 x - 3 y = 13$

$7 x - 2 y = 20$

EASY

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

X and Y

together have

₹ 1300

. If

₹ 10

less than three-fifth of the amount

X

is equal to half of the amount

Y

, then how much does

X

have?

EASY

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

Find the value of

x - y

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

EASY

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

Find the value of

x

after solving the following equation.

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

EASY

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

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.

MEDIUM

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

Solve the following system of linear equations:

$x + y = 3$

$4 x - 3 y = 26$

EASY

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

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?

MEDIUM

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

If we add

1

to the numerator and subtract

1

from the denominator, a fraction reduces to

1

. It becomes

\frac{1}{2}

if we only add

1

to the denominator. What is the fraction?

MEDIUM

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

A total of

57

sweets were distributed among

10

children such that each girl gets

6

sweets and each boy gets

5

sweets. Total number of boys is _____.

EASY

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

x + y = 5

and

x - y = 1

, then find the value of

x

HARD

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

$5$ 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.

EASY

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

A boat takes

10 h o u r s

to travel

30 k m

upstream and

44 k m

downstream, but it takes

13 h o u r s

to travel

40 k m

upstream and

55 k m

downstream. Find the speed of the boat in still water and the speed of the stream.

MEDIUM

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

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)

MEDIUM

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

Find the number of solutions of a pair of linear equation

4 x - 9 y + 13 = 0

and

2 x + 3 y - 13 = 0

MEDIUM

Mathematics>Algebra>Simultaneous Equations>Linear Equations Having Two Variables and their Solutions

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.

0x+0y+k= 0, k≠0 is a linear equation.

Important Questions on Simultaneous Equations

Learn and Prepare for any exam you want !

$0 x + 0 y + k = 0$ , $(k \neq 0)$ is a linear equation.