Question

How do you solve the following system?: `3x -6y =21, -x -3y = -7`

Answer 1

`x= 7` and `y = 0`

Explanation:

`3x -6y =21` -----------Let this be equation(1), and
`-x -3y = -7` ---------- Let this be equation(2)

From (2), by transposition method, we have :

`-x -3y = -7`

`-x = -7+3y`

`x = 7-3y` ---------------let this be equation (3).

Substitute vale of `x` from equation (3) in equation (1):

`3x -6y =21`

`3(7-3y) -6y =21`

`21 -9y -6y = 21`

`21 - 15y = 21`

`-15 y = 21-21`

`y = 0/-15`

`y =0`

From (3) , we can get value of `x`:

`x = 7-3y`

`x = 7-3(0)`

`x = 7-0`

`x = 7`

therefore we have:

`x= 7` and `y = 0`

Cross check by substituting values of `x`and `y` in equation (2):
`-x -3y = -7`
`-7 -3(0) = -7`
`-7 -0 = -7`
`-7 = -7`