# Linear Equation 18

### From Homeworkwiki

**Solve: **

**(i) x + y = 7**

**3 x - 2 y = 11**

**(ii) 8 x - 3 y = 1**

**34 x - 3 y = 14**

**Solution:**

(i) x + y = 7 => y = 7 - x

3 x - 2 y = 11 => 3 x - 2 (7 - x) = 11

=> 3 x - 14 + 2 x = 11

= > 5 x = 25 and x = 5

y = 7 - x => y = 7 - 5 = 2

Therefore, **Solution is : x = 5 and y = 2**

**Alternative method:**

Instead of finding the value of y in terms of x, if we find the value of x in terms of y and proceed as above, the result will remain the same. For this:

x + y = 7 => x = 7 - y

3 x - 2 y = 11 => 3 (7 - y) - 2 y = 11

=> 21 - 3 y - 2 y = 11

=> - 5 y = - 10 and y = 2

x = 7 - y => x = 7 - 2 = 5

Therefore, **Solution is : x = 5 and y = 2**

(ii) 8 x - 3 y = 1 => 8 x = 1 + 3 y and x = (1 + 3 y) / 8

34 x - 3 y = 14 => 34 [ (1 + 3 y) / 8 ] - 3 y = 14

=> ( 34 + 102 y - 24 y ) / 8 = 14

=> 78 y = 112 - 34 = 78 and y = 1

x = ( 1 + 3 y ) / 8 = ( 1 + 3 X 1 ) / 8 = 1 / 2

Therefore, **Solution is : x = 1 / 2 and y = 1**