Question

Solve the following systems of equations .

Chapter : Pair of linear equations in 2 variables.

Answer fast.

( No need of spam answers )​

Answer 1

Solution :

43.

The given equations are

152x - 378y = - 74 .....(i)

- 378x + 152y = - 604 .....(ii)

Adding (i) and (ii), we get

152x - 378y - 378x + 152y = - 74 - 604

or, 152 (x + y) - 378 (x + y) = - 678

or, (152 - 378) (x + y) = - 678

or, (- 226) (x + y) = - 678

or, x + y = 3 .....(iii)

From (i), we get

152x - 378 (3 - x) = - 74, by (i)

or, 152x - 1134 + 378x = - 74

or, 530x = - 74 + 1134

or, 530x = 1060

or, x = 2

Putting x = 2 in (iii), we get

2 + y = 3

or, y = 1

Therefore, the required solution is

x = 2 , y = 1.

45.

The given equations are

23x - 29y = 98 .....(i)

29x - 23y = 110 .....(ii)

Now, (i) + (ii) gives

23x - 29y + 29x - 23y = 98 + 110

or, 23 (x - y) + 29 (x - y) = 208

or, (23 + 29) (x - y) = 208

or, 52 (x - y) = 208

or, x - y = 4 .....(iii)

From (i), we get

23 (y + 4) - 29y = 98, by (iii)

or, 23y + 92 - 29y = 98

or, 6y = - 6

or, y = - 1

Putting y = - 1 in (iii), we get

x - (- 1) = 4

or, x + 1 = 4

or, x = 3

Therefore, the required solution is

x = 3 , y = - 1.

46.

The given equations are

x - y + z = 4 .....(i)

x - 2y - 2z = 9 .....(ii)

2x + y + 3z = 1 .....(iii)

(i) - (ii) gives

x - y + z - x + 2y + 2z = 4 - 9

or, y + 3z = - 5 .....(iv)

From (iii), we get

2x - 5 = 1, by (iv)

or, 2x = 6

or, x = 3

Putting x = 3 in (i), we get

3 - y + z = 4

or, - y + z = 1 .....(v)

(iv) + (v) gives

y + 3z - y + z = - 5 + 1

or, 4z = - 4

or, z = - 1

From (v), we get

- y - 1 = 1

or, y = - 2

Therefore, the required solution is

x = 3 , y = - 2 & z = - 1.

48.

The given equations are

21x + 47y = 110 .....(i)

47x + 21y = 162 .....(ii)

(i) + (ii) gives

21x + 47y + 47x + 21y = 110 + 162

or, 21 (x + y) + 47 (x + y) = 272

or, (21 + 47) (x + y) = 272

or, 68 (x + y) = 272

or, x + y = 4 .....(iii)

From (i), we get

21x + 47 (4 - x) = 110, by (iii)

or, 21x + 188 - 47x = 110

or, (21 - 47) x = 110 - 188

or, - 26x = - 78

or, x = 3

Putting x = 3 in (iii), we get

3 + y = 4

or, y = 4 - 3

or, y = 1

Therefore, the required solution is

x = 3 , y = 1.

Answer 2

Answer:

Refer to the attachment for ur answer dear...

Nice questions.....