Q. 44.2( 25 Votes )

# Solve the following simultaneous equations.

i.

ii.

iii.

Answer :

(i)

⇒ 4x + 3y = 48 eq.[1]

⇒ 2x - 3y = 4 eq.[2]

Adding eq.[1] and eq.[2], we get

⇒ 4x + 3y + 2x - 3y = 48 + 4

⇒ 6x = 52

Using this in eq.[1], we have

⇒ 104 + 9y = 144

⇒ 9y = 40

(ii)

⇒ x + 15y = 39

⇒ x = 39 - 15y eq.[1]

⇒ 4x + y = 38

Using eq.[1], we have

⇒ 4(39 - 15y) + y = 38

⇒ 156 - 60y + y = 38

⇒ 59y = 118

⇒ y = 2

Putting this value in eq.[2]

⇒ x = 39 - 15(2)

⇒ x = 39 - 30

⇒ x = 9

(iii)

⇒ 2y + 3x = 13xy eq.[1]

⇒ 5y - 4x = -2xy eq.[2]

Multiplying eq.[1] by 4 both side, and Multiplying eq.[2] by 3 both side, we get

8y + 12x = 52xy eq.[3]

15y - 12x = -6xy eq.[4]

Adding eq.[3] and eq.[4]

⇒ 8y + 12x + 15y - 12x = 52xy - 6xy

⇒ 23y = 46xy

⇒ 1 = 2x

Putting this in eq.[1]

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Solve the following simultaneous equations.

i.

ii.

iii.

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