Question

How do you solve `5y – x – 6 = 0` and `-3x + 6y = -9`?

Answer 1

`x=9, y=3`

Explanation:

First Method, using substitution

By rearranging the first equation we have,

`x = 5y -6`

substitute value of `x` in second equation

`-3*(5y -6) + 6y = -9`

`-15y +18 + 6y = -9`

`-9y +18 = -9`

`rArry-2 = 1`
`or y = 3`

by substituting value of `y` in either of the equations
we have

`x = 9`

Second Method,
Multiply first equation with 3,

`3*(5y-x-6)=0`

`15y-3x-18=0`

Now subtract LHS of the second equation from the LHS above equation and do the same with the RHS,

`(15y-3x-18)-(-3x+6y) = 0-(-9)`

`15y -3x -18 +3x-6y=9`

`9y -18 =9`
`rArr y =3`

and by substituting `y` in either of the equations we have

`x=9`