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

x + y = 5 and 2x – 3y = 4

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#### Solution

*x* + *y* =5 and 2*x* –3*y* = 4

By elimination method

x + y =5 ... (i)

2x –3y = 4 ... (ii)

Multiplying equation (i) by (ii), we get

2x + 2y = 10 ... (iii)

2x –3y = 4 ... (ii)

Subtracting equation (ii) from equation (iii), we get

5y = 6

y = `6/5`

Putting the value in equation (i), we get

`x = 5 - (6/5) = 19/5`

Hence, `x = 19/5 and y = 6/5`

By substitution method

x + y = 5 ... (i)

Subtracting y both side, we get

x = 5 - y ... (iv)

Putting the value of x in equation (ii) we get

2(5 – y) – 3y = 4

-5y = - 6

`y = (-6)/-5`

= `y = 6/5`

Putting the value of y in equation (iv) we get

`x = 5 – 6/5`

`x = 19/5`

Hence, `x = 19/5` and `y = 6/5` again

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