Question

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

3x – 5y – 4 = 0 and 9x = 2y + 7

Answer 1

3x – 5y – 4 = 0 and 9x = 2y + 7

By elimination method

3x – 5y – 4 = 0

3x – 5y = 4     ...(i)

9x = 2y + 7

9x – 2y = 7    ...(ii)

Multiplying equation (i) by 3, we get

9x – 15y = 12    ...(iii)

9x – 2y = 7         ...(ii)

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

-13y = -5

y = `-5/13`

Putting value in equation (i), we get

3x – 5y = 4     ...(i)

`3x - 5(-5/13) = 4`

Multiplying by 13 we get

39x + 25 = 52

39x = 27

x = `27/39`

x = `9/13`

Hence, our answer is `x = 9/13 and y = - 5/13`

By substitution method

3x - 5y- 4 = 0

9x - 2y - 7 = 0

`y = (3x - 4)/5`

Putting `y = (3x - 4)/5-7 = 0`

45x - 6x + 8 - 35 = 0

39x = 27

x = `27/39`

x = `9/13`

Putting x = `9/13` 

y = `(3xx9/13 - 4)/5`

y = `(27 - 52)/65`

y = `-25 /65`

y = `-5/13`

Hence, x = `9/13` and y = `-5/13`