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Class 12-science RD SHARMA Solutions Maths Chapter 8: Solution of Simultaneous Linear Equations

Solution of Simultaneous Linear Equations Exercise Ex. 8.1

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 1(iv)

Solution 1(v)

Solution 1(vi)

Solution 2(i)

Solution 2(ii)

Solution 2(iii)

Solution 2(iv)

Solution 2(v)

Solution 2(vi)

Solution 2(vii)

Solution 2(viii)

Solution 2(ix)

Solution 2(x)

Solution 2(xi)

Solution 2(xii)

Solution 2(xiii)

Solution 2(xiv)

Solution 3(i)

Solution 3(ii)

Solution 3(iii)


Solution 3(iv)


Solution 3(v)


Solution 3(vi)


Solution 4(i)

Solution 4(ii)

Solution 4(iii)

Solution 4(iv)

Solution 4(v)

Solution 4(vi)

Solution 5

Solution 6

Solution 7

Solution 8(i)

Solution 8(ii)

Solution 8(iii)

Solution 8(iv)

Solution 8(v)

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

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

Solution 15

Solution 16

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

Solution 17

Solution 18

Solution 19

Solution 20

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

As per the data in the question, we get

Solution 8(vi)

  

Therefore, A is invertible.

Let Cij be the co-factors of the elements aij.

  

   

Now, the given system of equations is expressible as

  

  

Here we have |AT| = |A| = -16 ≠ 0

Therefore, the given system of equations is consistent with a unique solution given by

  

Solution 8(vii)

  

Let

Now,

  

Now, the given system of equations is expressible as

  

  

Here we have |BT| = |B| = -1 ≠ 0

Therefore, the given system of equations is consistent with a unique solution given by

Hence, x = 36, y = 5 and z = -15.

Solution 21

From the given information, we can form a matrix as follows

  

Applying R2 R2 - 4R1, R3 R3 - 6R1

  

Applying R3 R3 + (-4R1)

  

From the above matrix form, we get

A + B + C = 21 … (i)

-B - 2C = -24 … (ii)

5C = 40

C = 8 … (iii)

Putting the value of C in (ii), we get

B = 8

Substituting B and C in (i), we get

C = 5

Hence, cost of variety 'A' pen is Rs. 8, cost of variety B pen is Rs. 8 and cost of variety 'C' pen is Rs. 5.

Solution of Simultaneous Linear Equations Exercise Ex. 8.2

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution of Simultaneous Linear Equations Exercise MCQ

Solution 1

  

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

  

Solution 7

Solution 8

Correct optio : (a)

x + 2y + 3z = 1

2x + y + 3z = 2

5x + 5y + 9z = 4

The determinant of the coefficient matrix begin mathsize 12px style open square brackets table row 1 2 3 row 2 1 3 row 5 5 9 end table close square brackets end style is

= -6-2 (18 - 15) + 3(10 - 5)

= -6 - 6 + 15

= 3 ≠ 0

The right hand side is also non zero.

The system has a unique solution.

Solution 9

Solution 10

Solution of Simultaneous Linear Equations Exercise Ex. 8VSAQ

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6