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

                    (iii)    3x - 5y -4 = 0\ \textup{and} \ 9x = 2y + 7

Answers (1)
P Pankaj Sanodiya

Elimination Method:

Given, equations

\\3x - 5y -4 = 0..........(1)\ \textup{and}\ \\9x = 2y + 7

\\\Rightarrow 9x - 2y -7=0........(2)

Now, multiplying (1) by 3 we, get

\\9x -15 y -12=0............(3)

Now, Subtracting (3) from (2), we get

9x-2y-7-9x+15y+12=0

\Rightarrow 13y+5=0

\Rightarrow y=\frac{-5}{13}

Putting this value in (1) we, get

3x-5(\frac{-5}{13})-4=0

\Rightarrow 3x=4-\frac{25}{13}

\Rightarrow 3x=\frac{27}{13}

\Rightarrow x=\frac{9}{13}

Hence,

 x=\frac{9}{13}\:and\:y=-\frac{5}{13}

Substitution method :

Given, equations

\\3x - 5y -4 = 0..........(1)\ \textup{and}\ \\9x = 2y + 7

\\\Rightarrow 9x - 2y -7=0........(2)

Now, from (2) we have,

y=\frac{9x-7}{2}.......(3)

substituting this value in (1)

3x-5\left(\frac{9x-7}{2} \right )-4=0

\Rightarrow 6x-45x+35-8=0

\Rightarrow -39x+27=0

\Rightarrow x=\frac{27}{39}=\frac{9}{13}

Substituting this value of x in (3)

\Rightarrow y=\frac{9(9/13)-7}{2}=\frac{81/13-7}{2}=\frac{-5}{13}

Hence,

x=\frac{9}{13}\:and\:y=-\frac{5}{13}

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