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  • Solve the following pair of linear equations by the elimination method and the substitution method : (ii) 3x + 4y = 10 and 2x - 2y = 2

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

                    (ii)    3x + 4 y = 10 \ \textup{and} \ 2x - 2y = 2

Answers (1)

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Elimination Method:

Given, equations

\\3x + 4 y = 10............(1) \ \textup{and}\\ \ 2x - 2y = 2..............(2)

Now, multiplying (2) by 2 we, get

\\4x -4 y =4............(3)

Now, Adding (1) and (3), we get

\\3x+4y+4x -4 y =10+4

\Rightarrow 7x=14

\Rightarrow x=2

Putting this value in (2) we, get

2(2)-2y=2

\Rightarrow 2y=2

\Rightarrow y=1

Hence,

 x=2\:and\:y=1

Substitution method :

Given, equations

\\3x + 4 y = 10............(1) \ \textup{and}\\ \ 2x - 2y = 2..............(2)

Now, from (2) we have,

y=\frac{2x-2}{2}=x-1.......(3)

substituting this value in (1)

3x+4(x-1)=10

\Rightarrow 3x+4x-4=10

\Rightarrow 7x=14

\Rightarrow x=2

Substituting this value of x in (3)

\Rightarrow y=x-1=2-1=1

Hence,

x=2\:and\:y=1

Posted by

Pankaj Sanodiya

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