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Mathematics

Solve the following pair of linear equations by the elimination method and the substitution method :

x + y = 5 and 2x - 3y = 4

Linear Equations

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Answer

Given,

x + y = 5 ………(1)

2x - 3y = 4 ……..(2)

Multiplying equation (1) by 3, we get :

3x + 3y = 15 ……..(3)

Adding equation (2) and (3), we get :

⇒ 2x - 3y + 3x + 3y = 4 + 15

⇒ 5x = 19

⇒ x = 195\dfrac{19}{5}

Substituting value of x in equation (1), we get :

⇒195+y=5⇒y=5−195⇒y=25−195⇒y=65.\Rightarrow \dfrac{19}{5} + y = 5 \\[1em] \Rightarrow y = 5 - \dfrac{19}{5} \\[1em] \Rightarrow y = \dfrac{25 - 19}{5} \\[1em] \Rightarrow y = \dfrac{6}{5}.

Hence, x = 195 and y=65\dfrac{19}{5} \text{ and y} = \dfrac{6}{5}.

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