# RD Sharma Solution CLass 12 Mathematics Chapter 8 Solution of Simultaneous Linear Equations

## Chapter 8 – Solution of Simultaneous Linear Equations Exercise Ex. 8.1

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 18
Solution 18
Question 19

Solution 19

Question 20

Solution 20

Question 21
Solution 21
Question 22
Solution 22
Question 23
Solution 23

Question 24
Solution 24

Question 25
Solution 25

Question 26
Solution 26

Question 27
Solution 27
Question 28
Solution 28
Question 29
Solution 29
Question 30
Solution 30
Question 31
Solution 31
Question 32
Solution 32
Question 33
Solution 33
Question 34
Solution 34
Question 35
Solution 35
Question 36
Solution 36
Question 37
Solution 37
Question 38
Solution 38
Question 39

Using A-1, solve the system of
linear equations

X – 2y = 10, 2x + y + 3z = 8 and -2y + z
= 7

Solution 39

Question 40

Solution 40

Question 41
Solution 41
Question 42
Solution 42
Question 43

Solution 43

Question 44
Solution 44
Question 45

The management committee of a
residential colony decided to award some of its members (say x) for honesty,
some (say y) for helping and others (say z) for supervising the workers to
keep the colony neat and clean. The sum of all the awardees is 12. Three
times the sum of awardees for cooperation and supervision added to two times
the number of awardees for honesty is 33. If the sum of the number of
awardees for honesty and supervision is twice the number of awardees for
helping others, using matrix method, find the number of awardees of each
category. Apart from these values, namely, honesty, cooperation and
supervision, suggest one more value which the management must include for
awards.

Solution 45

Question 46

A school wants to award its students
for the values of Honesty, Regularity and Hard work with a total cash award
of Rs. 6000. Three times the award money for Hard work added to that given
for honesty amounts to Rs. 11000. The award money given for Honesty and Hard work
together is double the one given for Regularity. Represent the above
situation algebraically and find the award for each value, using matrix
method. Apart from these values, namely, Honesty, Regularity and Hard work, suggest
one more value which the school must include for awards.

Solution 46

The school can include
an award for creativity and extra-curricular activities.

Question 47

Two institutions decided to award
their employees for the three values of resourcefulness, competence and
determination in the form of prizes at the rate of Rs. x, Rs. y and Rs. z respectively per person. The first
institution decided to award respectively 4, 3 and 2 employees with a total prize money of Rs. 37000 and the second
institution decided to award respectively 5, 3 and 4 employees with a total
prize money of Rs. 47000. If all the three prizes per person together amount
to Rs. 12000, then using matrix method find the value of x, y and z. What values are described in these
equations?

Solution 47

Question 48

Two factories decided
to award their employees for three values of (a) adaptable to new techniques,
(b) careful and alert in difficult situations and (c) keeping calm in tense
situations, at the rate of Rs. x,
Rs. y and Rs. z per person respectively. The first factory decided to honour respectively 2, 4 and 3 employees with a total prize money of Rs. 29000. The second factory
decided to honour respectively 5, 2 and 3 employees
with the prize money of Rs. 30500. If the three prizes per person together
cost Rs 9500, then

(i)
represent the above situation by matrix equation and
form linear equations using matrix multiplication.

(ii) Solve these
equations using matrices.

(iii) Which values are
reflected in the questions?

Solution 48

Keeping calm in a tense
situation is more rewarding than carefulness, and carefulness is more

Question 49

Two schools A and B want to award
their selected students on the values of sincerity, truthfulness and
helpfulness. The school A wants to award Rs. x each Rs. y each and
Rs. z each for the three respective
values to 3, 2 and 1 students respectively with a total
award money of Rs. 1,600. School B wants to spend Rs 2,300 to award its 4, 1
and 3 students on the respective values (by giving the same award money to
the three values as before). If the total amount of award for one prize on
each value is Rs 900, using matrices, find the award money for each value.
Apart from these three values, suggest one more value which should be
considered for award.

Solution 49

Question 50

Two schools P and Q want to award
their selected students on the values of Discipline, Politeness and
Punctuality. The school P wants to
award Rs. x each, Rs. y each and Rs. z each for the three respectively values to its 3, 2 and 1
students with a total award money of Rs. 1,000. School Q wants to spend Rs. 1,500 to award its 4, 1 and 3 students on
the respective values (by giving the same award money for three values as
before). If the total amount of awards for one prize on each value is Rs.
600, using matrices, find the award money for each value. Apart from the
above three values, suggest one more value for awards.

Solution 50

Question 51

Two schools P and Q want to award
their selected students on the values of Tolerance, Kindness and Leadership.
The school P wants to award Rs. x each, Rs. y each and Rs. z each
for the three respectively values to its 3, 2 and 1 students with a total
award money of Rs. 2,200. School Q
wants to spend Rs. 3,100 to award its 4, 1 and 3 students on the respective
values (by giving the same award money to the three values as school P). If the total amount of award for
one prize on each values is Rs. 1,200, using matrices, find the award money
for each value. Apart from these three values, suggest one more value which
should be considered for award.

Solution 51

Question 52

A total amount of Rs. 7000 is
deposited in three different saving bank accounts with annual interest rates
5%, 8% and 8.5% respectively. The total annual interest from these three
accounts is Rs. 550. Equal amounts have been deposited in the 5% and 8%
savings accounts. Find the amount deposited in each of the three accounts,
with the help of matrices.

Solution 52

Let the amount
deposited be x, y and z respectively.

As per the data in the
question, we get

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

## Chapter 8 – Solution of Simultaneous Linear Equations Exercise MCQ

Question 1

The system of equation x + y + z = 2, 3x – y + 2z = 6 and 3x + y + z = -18 has

a. a unique solution

b. no solution

c. an infinite number of solutions

d. zero solution as the only solution

Solution 1

Question 2

a. 3

b. 2

c. 1

d. 0

Solution 2

Question 3

a.

b.

c.

d.

Solution 3

Question 4

The number of solutions of the system of equations:

, is

a. 3

b. 2

c. 1

d. 0

Solution 4

Question 5

The system of linear equations:

Has a unique solution if

a. k ≠ 0

b. -1 < k < 1

c. -2 < k < 2

d. k = 0

Solution 5

Question 6

Consider the system of equations:

a1x + b1y + c1z = 0

a2x + b2y + c2z = 0

a3x + b3y + c3z = 0.

a. more than two solutions

b. one trivial and one non-trivial solutions

c. no solution

d. only trivial solution (0, 0, 0)

Solution 6

Question 7

Let a, b , c be positive real numbers. The following system of equations in x, y and z

a. no solutions

b. unique solution

c. there is no solution

d. finitely many solutions

Solution 7

Question 8

For the system of equations :

x + 2y + 3x = 1

2x + y + 3z = 2

5x + 5y + 9z = 4

a. there is only one solution

b. there exists infinitely many solution

c. there is no solution

d. none of these

Solution 8

Question 9

The existence of the unique solution of the system of equations:

x + y +z = λ

5x – y + μz = 10

2x + 3y – z = 6 depends on

a. μ only

b. λ only

c. λ and μ both

d. neither λ nor μ

Solution 9

Question 10

The system of equations:

x + y + z = 5

x + 2y + 3z = 9

x + 3y + λz = μ

Has a unique solution, if

a. λ = 5, μ = 13

b. λ ≠ 5

c. λ = 5, μ ≠ 13

d. μ ≠ 13

Solution 10

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