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Question
Solve the following set of simultaneous equation.
x + y = 4 ; 2x - 5y = 1
Solution 1
x + y = 4 ...(I)
2x - 5y = 1 ...(II)
From (I) we have
x = 4 - y
Putting this value of x in (II)
2 (4 - y) - 5y = 1
⇒ 8 - 2y - 5y = 1
⇒ 8 - 7y = 1
⇒ 8 - 1 = 7y
⇒ 7 = 7y
⇒ y = 1
Putting the value of y in (I) we have
x + 1 = 4
⇒ x = 3
Thus, (x, y) = (3, 1)
Solution 2
x + y = 4 ...(i)
2x - 5y = 1 ...(ii)
On multiplying both sides of equation (i) by 5,
5x + 5y = 20 ...(iii)
By adding equations (ii) and (iii),
5x + 5y = 20 ...(iii)
2x - 5y = 1 ...(ii)
7x = 21
∴ x = `21/7`
∴ x = 3
Substituting x = 3 in equation (i), we get
∴ x + y = 4
∴ 3 + y = 4
∴ y = 4 - 3
∴ y = 1
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