Question

solve the following no spams ​

Answer 1

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Answer 2

1.

Eqn (i): 2x + 3y = 11

Eqn (ii): 4x - y = 5

Obtain value of y from eqn (ii):

4x - y = 5

y = 4x + 5

Put this value of y in eqn (i):

2x + 3y = 11

=> 2x + 3(4x + 5) = 11

=> 2x + 12x + 15 = 11

=> 14x = -4

=> x = -2/7

y = 4x + 5

=> y = 4(-2/7) + 5

=> y = (-8 + 35)/7

=> y = 27/7

2.

Eqn (i): x - y = -1

Eqn (ii): 2x + y = 10

Obtain value of x from eqn(i):

x = y - 1

Put this in eqn(ii):

2x + y = 10

=> 2(y - 1) + y = 10

=> 2y - 2 + 2y = 10

=> 4y = 12

=> y = 3

x = y - 1

=> x = 2

3.

Eqn(i): 4x + 6y = 18

Eqn(ii): 2x + 3y = 9

This equation can't 've solved. This is because, they are equivalent equations

If you multiply eqn(ii) by 2, you get the result as eqn(i). Thus, the data is insufficient.

4.

Eqn(i): 2x + 3y = 7

Eqn(ii): 2x + 6y = 5

Solve eqn(i) for x:

x = (7 - 3y)/2

Put in eqn(ii) and solve:

2x + 6y = 5

2(7 - 3y)/2 + 6y = 5

14 - 6y + 12y = 10

14 + 6y = 10

6y = -4

y = -2/3

x = (7 - 3y)/2

x = (7 - (-2))/2

x = 9/2

5.

Eqn(i): 3x - 7y = -10

Eqn(ii): y - 2x = 3

Obtain y from eqn(i):

y = (3x + 10)/7

Put this in eqn(ii) and solve:

(3x + 10)/7 - 2x = 3

3x + 10 - 14x = 21

-11x = 11

x = -1

y = (3(-1) + 10)/7

y = 1

6.

Eqn(i): x + 2y = 3/2

Eqn(ii): 2x + y = 3/2

Obtain x from eqn(i):

x = 3/2 - 2y

x = (3 - 4y)/2

Put in eqn(ii) and solve:

3 - 4y + y = 3/2

6 - 6y = 3

6y = 3

y = 1/2

x = (3 - 2)/2

x = 1/2

7.

Eqn(i): 3x + 6y = 7

Eqn(ii): 9x + 3y = 11

Obtain x from eqn(i):

x = (7 - 6y)/3

Put x in eqn(ii) and solve:

3(7 - 6y) + 3y = 11

21 - 18y + 3y = 11

15y = 10

y = 2/3

x = (7 - 4)/3

x = 1

8.

Eqn(i): 3x - 4y = 10

Eqn(ii): 4x + 3y = 5

Obtain x from eqn(i):

x = (10 + 4y)/3

Put this in eqn(ii) and solve:

4(10 + 4y)/3 + 3y = 5

40 + 16y + 9y = 15

25y = -25

y = -1

x = (10 - 4)/3

x = 6/3

x = 2

HOPE IT HELPS!!