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Solve the following pair of linear equations by the elimination method and the substitution method : (i) x + y = 5 and 2x - 3y = 4

Q1.    Solve the following pair of linear equations by the elimination method and the substitution method :

                    (i)    x + y =5 \ \textup{and} \ 2x - 3y = 4

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Elimination Method:

Given, equations

\\x + y =5............(1) \ \textup{and} \\ \ 2x - 3y = 4........(2)

Now, multiplying (1) by 3 we, get

\\3x +3 y =15............(3)

Now, Adding (2) and (3), we get

\\2x-3y+3x +3 y =4+15

\Rightarrow 5x=19

\Rightarrow x=\frac{19}{5}

Substituting this value in (1) we, get

\frac{19}{5}+y=5

\Rightarrow y=5-\frac{19}{5}

\Rightarrow y=\frac{6}{5}

Hence,

 x=\frac{19}{5}\:and\:y=\frac{6}{5}

Substitution method :

Given, equations

\\x + y =5............(1) \ \textup{and} \\ \ 2x - 3y = 4........(2)

Now, from (1) we have,

y=5-x.......(3)

substituting this value in (2)

2x-3(5-x)=4

\Rightarrow 2x-15+3x=4

\Rightarrow 5x=19

\Rightarrow x=\frac{19}{5}

Substituting this value of x in (3)

\Rightarrow y=5-x=5-\frac{19}{5}=\frac{6}{5}

Hence,

x=\frac{19}{5}\:and\:y=\frac{6}{5}

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