#### Solve the linear equations:

(i) x + y = 14

x – y = 4

(ii) s – t = 3

s/3 + t/2 = 6

(iii) 2x + 3y = 9

3x + 4y = 5

(iv) 3x – 5y = 4

9x – 2y = 7

**Solution:**

(i) x + y = 14

x – y = 4

It can be written as

x = 4 + y

By substituting the value in the above equation

4 + y + y = 14

By further calculation

2y = 14 – 4 = 10

Dividing by 2

y = 10/2 = 5

So we get

x = 4 + 5 = 9

Hence, x = 9 and y = 5.

(ii) s – t = 3

s/3 + t/2 = 6

By taking LCM

2s + 3t = 6 × 6 = 36

We know that

s – t = 3 …. (1)

2s + 3t = 36 ….. (2)

So we get

s = 3 + t …. (3)

By substituting the value of s in equation (2)

2 (3 + t) + 3t = 36

By further calculation

6 + 2t + 3t = 36

So we get

5t = 36 – 6 = 30

By division

t = 30/5 = 6

Substituting t in equation (3)

s = 3 + 6 = 9

Hence, s = 9 and t = 6.

(iii) 2x + 3y = 9 …. (1)

3x + 4y = 5 ….. (2)

Equation (1) can be written as

2x = 9 – 3y

x = (9 – 3y)/ 2 …. (3)

By substituting the value of x in equation (2)

3 × (9 – 3y)/ 2 + 4y = 5

By further calculation

(27 – 9y)/ 2 + 4y = 5

By taking LCM

27 – 9y + 8y = 10

So we get

-y = – 17

y = 17

Substituting y in equation (3)

x = [9 – (3 × 17)]/ 2

By further calculation

x = (9 – 51)/ 2

x = – 21

Hence, x = – 21 and y = 17.

(iv) 3x – 5y = 4 ….. (1)

9x – 2y = 7 …. (2)

Multiply equation (1) by 3

9x – 15y = 12

9x – 2y = 7

By subtracting both the equations

– 13y = 5

y = -5/13

Equation (1) can be written as

3x – 5y = 4

x = (4 + 5y)/ 3 ….. (3)

By substituting the value of x in equation (2)

9 [(4 + 5y)/ 3] – 2y = 7

By further calculation

12 + 15y – 2y = 7

13y = – 5

So we get

y = -5/13

Substituting y in equation (3)

Hence, x = 9/13 and y = – 5/13.

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