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Solve the following simultaneous equations.x3+y4=4 ; x2-y4=1 - Algebra

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Sum

Solve the following simultaneous equations.
`x/3 + y/4 = 4; x/2 - y/4 = 1`

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Solution

`x/3 + y/4 = 4`                                .....(I)

`x/2 - y/4 = 1`                                ......(II)  

Multiplying (I) with LCM of 3 and 4 which is 12, we get
`4x + 3y = 48`                              .......(III)
Multiplying (II) with LCM of 2 and 4 which is 4, we get
2x - y = 4                                     .......(IV)
Multiplying (IV) with 2
4x - 2y = 8                                  .......(V)
Subtracting (V) from (III)
5y = 40
⇒ y = 8

Putting this value of y in (IV) we get
2x - 8 = 4
⇒ 2x = 12
⇒ x = 6.

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Elimination Method
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APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 5 Linear Equations in Two Variables
Problem Set 5 | Q 4.1 | Page 91
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