Question

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

x + y = 5 and 2x – 3y = 4

Answer 1

x + y = 5 and 2x – 3y = 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`.