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Question
By equating coefficients of variables, solve the following equation.
4x + y = 34 ; x + 4y = 16
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Solution
4x + y = 34 ...(I)
x + 4y = 16 ...(II)
Adding (I) and (II) we get,
4x + y = 34
x + 4y = 16
5x + 5y = 50
⇒ x + y = 10 ...(III)
Subtracting (II) from (I) we get,
4x + y = 34
x + 4y = 16
- - -
3x - 3y = 18
⇒ x - y = 6 ...(IV)
Adding (III) and (IV) we get,
x + y = 10
x - y = 6
2x = 16
⇒ x = 8
Putting the value of x in (I) we get,
∴ 4x + y = 34
⇒ 4 (8) + y = 34
⇒ y = 34 - 32
⇒ y = 2
Thus, x = 8, y = 2
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