Question

33x + 32y = 34 ; 32x + 33y =31

Answer 1

Solution :

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Given :

33x + 32y = 34  ....(i)

32x + 33y = 31  .....(ii)

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To Find :

 Values of x & y

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⇒ By adding both the equation,

We get,.

⇒ (33x + 32y) + (32x + 33y) = 34 + 31

⇒ 33x + 32x + 32 y + 33y = 65

⇒ 65x + 65y = 65

⇒ 65(x + y) = 65(1)

⇒ x + y = 1 ....(iii)

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By subtracting (ii) from (i),

We get,.

⇒ (33x + 32y) - (32x + 33y) = 34 - 31

⇒ 33x - 32x + 32y - 33y = 3

⇒ x - y = 3 ....(iv)

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By adding (iii) & (iv),

We get,.

⇒ (x + y) + (x - y) = 1 + 3

⇒ x + y + x - y = 4

⇒ 2x = 4

⇒ x = 2

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By substituting the value of x in (iii),

We get,

⇒ x + y = 1

⇒ 2 + y = 1

⇒ y = 1 - 2

⇒ y = -1

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Answer 2

33x + 32y = 34 |→*33
32x + 33y = 31 |→*32

1089x + 1056y = 1122   -----[1]
1024x + 1056y =  992   ------[2]

subtracting eq. [1] - [2]

   1089x + 1056y = 1122
  -1024x  - 1056y = -992
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     65x    -  0       = 130
               
                           x=130/65
                           x=2